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VARIATION IN THE ACHIEVEMENTS 
OF PUPILS 



A STUDY OF THE ACHIEVEMENTS OF PUPILS IN 

THE FIFTH AND SEVENTH GRADES, AND 

IN CLASSES OF DIFFERENT SIZES 



By 
CHARLES HERBERT ELLIOTT, Ph.D. 



TEACHERS COLLEGE. COLUMBIA UNIVERSITY 
CONTRIBUTIONS TO EDUCATION. No 72 



PUBLISHED BY 

®*acIi?rB Olnlbgf, Olnlttmhta lnitipr0itg 

NEW YORK CITY 

1914 






Copyright, 1915, by Charles Herbert Elliott 

COPYmGl*T Off 15!. 
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fM -7 i9l5 

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CONTENTS 

CHAPTER PAGE 

Introduction 1 

I. The Measurement of Educational Efficiency 3 

II. The Data. The Tests. The Method of Scoring 7 

The Tests and Their Administration 8 

Spelling 8 

Handwriting 10 

English Composition 11 

Range of Vocabulary 13 

Arithmetic 14 

Other Data Collected at the Time the Tests were Given 15 

The Method of Scoring ' 18 

III. Standards of Achievement for Fifth and Seventh Grade 

Pupils 21 

Arithmetic 26 

English Composition 30 

Spelling 31 

Handwriting 35 

Range of Vocabulary 37 

IV. Attainment in Classes 3S 

V. The Measurement of Class Size 47 

Attainment and Overlapping of the Classes in which Standard 

Measures were Taken 47 

Overlapping within the Separate Systems 50 

Attainment, Variability and Growth in Other Systems 56 

Class Size, Promotion Rate and Expenditiu-e 63 

Investigations of Class Size 64 

VI. Summary and Suggested Interpretations of the Data 77 

appendix 

I. General Directions for the Administration of the Tests 92 

II. Samples of Other Tests 99 

III. Preliminary List of Composition Subjects 105 

Notes 106 

IV. Notes on Measurement of Class Size 107 

V. Bibliography 109 



ACKNOWLEDGMENTS 

The writer finds himself under obligations to so many persons 
that it is impossible to acknowledge his indebtedness to the in- 
dividual teachers and superintendents who have very cheerfully 
co-operated in the making of this study. His greatest obliga- 
tion is to Professor G. D. Strayer, who suggested the topic and 
directed the study. He is under many obligations to Professor 
E. L. Thorndike for extended help in the various problems of 
measurement, and to Professors James McKeen Cattell and 
Milo B. Hillegas for many helpful criticisms. To Professor 
Franklin T. Baker he is indebted for valuable assistance in 
formulating the composition test. Special aid was rendered by 
Superintendents Ira T. Chapman of Norwalk, Connecticut, 
James N. Muir of Orange, New Jersey, and Don C. Bliss of 
Montclair, New Jersey, who placed at the disposal of the writer 
much valuable data bearing upon the problem. Finally he 
desires to acknowledge a great debt to Professor Henry Suz- 
zallo for many helpful suggestions in the interpretation of 
the data. 

C. H. E. 



VARIATION IN THE ACHIEVEMENTS OF PUPILS 

INTRODUCTION 

In the past decade much has been done in the development 
of units and scales for the measurement of educational pro- 
ducts. No less important has been the development of methods 
of applying these and other instruments of scientific procedure 
to the problems of education. This whole movement is but a 
part of a larger one which has in recent years extended the 
scope of the applied sciences and utilized the principles of 
science in the improvement of many lines of human endeavor. 

In the succeeding pages there is presented a sample study 
which utilizes those methods of educational measurement that 
may be applied to ordinary school situations. The achieve- 
ments of more than seventeen hundred children in the fifth 
and seventh grades have been measiired in the several subjects 
of arithmetic, English composition, spelling, handwriting, and 
range of vocabulary. The results are gathered into tables and 
may be used as tentative standards for evaluating the work 
of a school system in these subjects. The achievements, the 
variabilities, and the amounts of growth are symptomatic of 
the performance of the children in these grades and may be 
used further as a starting point for the derivation of better 
standards. These summaries are presented in Chapter III and 
are not repeated in the last pages of this study, i 

One further problem has been considered. The size of class 

in which the children have been taught has been studied from 

the records of the seventeen hundred pupils. To supplement 

these, records of more than ten thousand children in four hundred 

forty-four classes have been utilized. These records include 

attainment in spelling and oral arithmetic, and measurements 

of growth by classes for a period of seventeen weeks in language 

and handwriting in two city school systems in which the testing 

1 It should be noted that all possible problems have not been studied. 
The influence of sex, age, and the like could have been studied in detail if 
the limits of the present investigation had permitted. 

1 



2 Variation in the Achievements of Pupils 

was done under the same conditions of supervision. The find- 
ings derived from a study of this phase of the problem are 
valid in so far as the nine systems are typical of American 
practice. 

One of the chief contributions which a study of this type 
can make is the method of standardized investigation which it 
develops. It offers a tentative standard for comparison in 
testing the efficiency of the same grades in other systems under 
survey. In order that the study may be of service to those 
who wish to make scientific measurements of school work in 
these subjects, a very carefully prepared list of the tests together 
with detailed directions for their administration and the evalu- 
ation of results is presented in the Appendix. 



CHAPTER I 
THE MEASUREMENT OF EDUCATIONAL EFFICIENCY 

In this age of scientific advancement we hear an insistent 
demand for the measurement of efficiency. The movement 
known as "scientific management" to-day affects not only the 
organization of industry but its methods are being incorporated 
into nearly every line of human endeavor and are now being 
applied in education. The notable contributions in educa- 
tional research in the past six years include many studies and 
methods that can be applied in the measurement of educa- 
tion with a precision comparable to that of some of the applied 
sciences. 

We may consider the measurement of educational efficiency 
from a great many angles. For many years, we have measured 
automatically the efficiency of higher education in the defini- 
tions of what constitutes an institution of higher learning which 
we find in the laws of the various states, in the definitions of 
the United States Bureau of Education, the Carnegie Founda- 
tion for the Advancement of Teaching and many voluntary 
associations that deal with this phase of education. Definitions 
and standards covering such elements as the amount of endow- 
ment, income, entrance requirements, curriculum, plant, time 
allotment and teaching staff have been formulated. In the 
field of secondary education the definitions of entrance require- 
ments formulated by agencies which deal with institutions of 
higher learning have been utilized as norms of attainment by 
the secondary school. Further, associations formed to deal 
primarily with secondary school problems and the accrediting 
body of various institutions of college grade, particularly the 
State universities of the Middle West, have formulated rather 
elaborate definitions and standards which cover such elements 



4 Variation in the Achievements of Pupils 

as plant, class size, time allotment, preparation and certifica- 
tion of teachers and the content of the curriculum. * 

Elementary education has not been standardized in the same 
manner. Aside from the standardization of curriculum at- 
tempted in 1895 by the Committee of Fifteen, nothing compar- 
able has been done. The studies of time allotment have been 
of little significance. But it should be noted that the most 
recent developments in methods of measurement and adminis- 
trative technique deal in great part with elementary education. 

In any study of the measurement of education we may deal 
with these more formal aspects. Or we may deal with those 
findings that have assisted in developing more adequate methods 
of studying the school population, children in school, health of 
children, the school plant, school receipts and expenditures 
and, as a by-product of these, the improvement of school 
records. Another course open to us is to study the achieve- 
ments of children in various school subjects. This enables us, 
by employing standard tests and the various units and scales of 
measurement that have been devised, to measure directly pro- 
ducts of children's work in these particular subjects and more 
indirectly to measure the process of education. This is the 
method that has been selected in the study here reported. 

The pioneer work of Rice, 2 Cornman,^ St one, ^ Courtis,'* and 

others « suggested the possibility of developing standard tests. 

The field of knowledge was not advanced beyond this point 

^ For excellent examples of this, see the reports of the North Central Asso- 
ciation of Colleges and Secondary Schools. See also the definitions of units 
and discussions of entrance requirements for universities which admit by 
certificate, e.g., Illinois, Wisconsin, Michigan. 

2 The Futihty of the Spelling Grind, The Forum, Vol. XXIII, pp. 163-172 
and 409-419. 

Educational Research: A Test in Arithmetic, The Forum, Vol. XXXIV, 
pp. 281-297. 

Causes of Success and Failure in Arithmetic, The Forum, Vol. XXXIV, 
pp. 437-452. 

Educational Research: The Results of a Test in Language, The Forum, 
Vol. XXXV, pp. 269-293. 

Language (continued): The Need of a New Basis in Education, The 
Forum, Vol. XXXV, pp. 440-457. 

3 Spelling in the Elementary School: An Experimental and Statistical 
Investigation. 

^Arithmetical Abilities and Some Factors Determining Them, Teachers 
College Contributions to Education, No, 19. 

^ The Courtis Tests, Series A. 

Final Report of the Committee on School Inquiry for New York City, Vol. 
I, pp. 397-546. 

•Bliss in Psychological Clinic, Vol. VI, No. 1, pp. 1-12, 



The Measurement of Educational Efficiency 5 

until Professor Thorndike in 1910 developed the first scale for 
the measurement of an educational product.' In his published 
description, Professor Thorndike presents scales for the meas- 
urement of the quality of handwriting of children in the ele- 
mentary grades and also for the measurement of the hand- 
writing of women. In the derivation of these scales, use was 
made of the methods devised by Galton, Pearson, Cattell and 
other students of variable quantities. Scores were derived from 
the judgments of educational experts. By a careful study of 
the variability of these ratings, and by utilizing the principle 
that differences equally often noticed are equal, relative values 
of the samples were determined and the scales formed. The 
handwriting scales consist of a series of samples of handwriting 
with which the specimens to be measured are compared. 

In 1911, Dr. L. P. Ayres, of the Russell Sage Foundation, 
derived and published a scale for the measurement « of legi- 
bility in handwriting. This scale was derived in a manner 
radically different from that utilized by Professor Thorndike. 
Legibility was measured in terms of the time that it takes 
competent judges to read samples of handwriting. After elim- 
inating the practice effect upon the time taken to read the 
samples, they were arranged along a scale of difficulty taken as 
a function of the time required to read the samples. From a 
comparison of the form of distribution of these samples with 
the normal surface of frequency, the values of the samples 
were obtained. 

In 1912, Professor Milo B. Hillegas of Teachers College 
derived a scale for the measurement of quality in English Com- 
position by young people. ^ The derivation of this scale was 
made by the same methods that had been utilized by Thorn- 
dike in the derivation of the handwriting scale. The completed 
scale represents a series of compositions with values from 
to 9.37. Compositions are graded by comparing the specimens 
with the series of samples which constitute the scale. 

In 1913, Dr. B. R. Buckingham, now statistician of the 
New York Board of Education, derived a scale for the measure- 

' This list merely summarizes the most significant studies in educational 
measurement. The literature of statistics and psychology includes much 
valuable material and many suggestive methods. 

8 Bulletin of the Division of Education, Russell Sage Foundation, 1912- 
No. 113. 

8 Teachers College Record, September, 1912. 



6 Variation in the Achievements of Pupils 

ment of spelling ability of children in grades three to eight 
inclusive. 1° Dr. Buckingham's method of deriving his scales 
utilizes in part the method discussed above, but, in addition, 
he studied the overlapping of grade upon grade, utilizing in 
these studies nearly ten thousand records. By the use of these 
scales, we are able to rate words in terms of * 'difficulty to spell." 
For example, "circus" and "carriage," "touch" and "surface" 
are approximately of equal difficulty. ^^ Dr. Buckingham has in 
the past few months extended the results of this study until he 
now has records of nearly twenty thousand children. He states 
that there is practically no change in the position of the words 
on the scales as originally printed. 

In 1913, Professor Thorndike derived by a method similar 
to the method utilized in the derivation of the handwriting 
scale, a scale for the measurement of ability in drawing^^ of 
children in the grades of the elementary school. In addition 
to this he has made in the past two years important contribu- 
tions to method in his suggestions of improved methods^' for 
handling and interpreting data and in his suggestive studies 
of expectancy. 14 

1° Spelling Ability, Its Measurement and Distribution, Teachers College 
Contributions to Education, 1913, No. 59. 

^* Measured by the per cent of fifth and fourth grade children respec- 
tively who spell the pairs correctly. The pairs are not at precisely the same 
point on Buckingham's scale. 

12 Teachers College Record, November, 1913. 

"Mental and Social Measurements, 1913 (second edition). 

" (a) Educational Diagnosis: Vice-Presidential Address, American Associa- 
tion for the Advancement of Science, 1912, Science, N. S. Vol. 37, Nos. 943 and 
946. For a discussion of the data on which a part of this address depends, 
see The Elimination of Pupils from the High Schools of New York, by Van 
Denburg, The Correlation of Mental Abilities, by Simpson, and Educational 
Administration, by Strayer and Thorndike. 

(b) Educational Administration, by Strayer and Thorndike. 

(c) Teachers College Alumni Bulletin, 1913. 



CHAPTER II 
THE DATA. THE TESTS. THE METHOD OF SCORING 

The selection of schools in which the testing has been done 
has been made upon the basis of a random sampling which 
would insure the inclusion of all types of schools, i.e., small 
city, medium sized city, suburban city, and large city. This 
random selection was extended sufficiently to be certain that 
the different levels of school population, such as poor American, 
good American, extraordinarily good American, foreign and 
low grade foreign, were included. To this end forty classes 
in fourteen schools in five groups have been critically studied. 
In addition to these there are presented four hundred forty- 
four class records of tests in language, handwriting, spelling 
and oral arithmetic. These records represent a random sam- 
pling from many more classes in two cities, one in New York 
and the other in Massachusetts, in which the testing was not 
done by the author but by an exceptionally competent super- 
intendent under controlled conditions. The papers were scored 
by an experienced teacher who at the same time is a competent 
statistical clerk. These classes included about ten thousand 
children. In the forty classes which are widely distributed 
in the schools of New York, New Jersey and New England, 
seventeen hundred twenty pupils have been measured in the 
five traits, arithmetic, spelling, English composition, penman- 
ship, and range of vocabidary. In several hundred instances, 
several scorings have been made of the work so that the num- 
ber of records of pupils actually utilized in this study is some- 
what more than twenty thousand. 

Although it is evident that the careful measurements which 
have been made of the seventeen hundred twenty children in 
forty classes, involving as wide a distribution as to territory, 
school population, and mental abilities, as is described above, 
are more than a sufficient basis for determining the symptoms of 
relationship between class size and attainment, nevertheless, 

7 



8 Variation in the Achievements of Pupils 

every possible source of material has been canvassed so far 
as the limits of this study would permit. 

Section 1 
The Tests and Their Administration 
In the following paragraphs are described the tests which have 
been selected, the reasons given for choosing them and the de 
tailed directions for their administration. In every instance^ the 
tests have been given by the author. Through the courtesy of 
the supervisory officers of all of the systems tested the writer was 
permitted to use the paper utilized by the school in its regular 
work in each of the subjects tested. For this reason no mention 
is made in the succeeding pages of the selection of paper. Pens 
were also generously supplied so that the conditions under which 
the pupils did their actual school work were not changed in any 
important detail. 2 

SPELLING 

Various studies of the spelling of school children have been 
made. The most important are those by Cornman,^ Rice,< 
Wallin,^ Buckingham, 6 and Thorndike and Earle.^ 

In his elaborate study of spelling Buckingham has been 
able by the methods utilized by Thorndike » to make fairly 
accurate scales for spelling ability for grades three to eight 
inclusive. A careful study of these scales has revealed the fact 
that certain words have an equivalence, that is, to spell 
** carriage" requires approximately the same amount of spelling 
ability as t o spell " believe." 

1 With the exception of Tests I, II and III in range of vocabulary, which 
were given by a trained investigator in a single room under the immediate 
supervision of the writer, and the tests in arithmetic in System D. 

2 Had this not been possible then a uniform paper and a imiform pen 
would have been selected. 

' Spelling in the Elementary School: An Experimental and Statistical 
Investigation. 

* The FutiHty of the Spelling Grind, The Forum, Vol. XXIII, pp. 163-172 
and pp. 409-419. 

6 Spelling Efficiency in Relation to Age, Grade and Sex, and the Question 
of Transfer. 

• Spelling Ability, Its Measurement and Distribution, Teachers College 
Contributions to Education, No. 59. 

' Heredity, Correlation and Sex Differences in School Abilities. Columbia 
University Contributions to Philosophy, Psychology and Education, Vol. 
XI, No. 2. 

8 Op. cit. 



Data Upon Which the Studies are Based 9 

The words selected are those that are spelled by approx- 
imately fifty per cent of the grade tested. They are equivalent 
in that sense although they do not stand at precisely the same 
point on Buckingham's scale. Comparisons of grade status 
may be made in terms of the per cent of the grade which spells 
correctly these median words or by the use of Buckingham's 
scale. 

DIRECTIONS FOR GIVING THE TESTS IN SPELLING 

Upon entering the classroom there was obtained from the 
teacher a sufficient amount of ruled paper such as was used for 
ordinary composition work to supply each pupil with one sheet. 
The paper was distributed by the regular monitors. These 
directions were then given: 

" Write your name in the upper right-hand corner of the 
sheet. Under this state whether you are a boy or a girl. Under 
this write the date of your birthday. Under this write the 
number of years old you were at your last birthday. 

" I wish you to write carefully some sentences which I shall 
dictate. Number them in order on the left." 

Sentences containing these standard words » were then 
dictated : 

Fourth Grade: 

wear, button, touch, surface. 
Fifth Grade: 

believe, loose, circus, carriage. 
Sixth Grade: 

saucy, whistling, beginning, succeed. 
Seventh Grade: 

ascending, slipped, imagine, character. 
Eighth Grade: 

peculiar, mixture, intelligent, occasion. 

In dictating the sentences each one was read through twice 
and then dictated in phrases as marked, allowing the number 
of seconds per phrase for writing indicated above each phrase. i" 
When the last sentence had been dictated, and time allowed for 
writing the last phrase, this signal was given: 

"All stop . Pens down. Blot your work. Monitors collect." 

^ Spelled correctly by approximately fifty per cent of the pupils in the 
grade. 
1° See Appendix. 



10 Variation in the Achievements of Pupils 

PENMANSHIP 

In the past six years, a large number of important studies of 
the teaching and rating of penmanship have been made. Refer- 
ence is made specifically to the work of Thompson," Houston," 
Ayres,i3 and Thorndike.i^ Professor Thorndike, during the 
years 1908-1910, developed the first scale for the measurement 
of handwriting. This scale and the one developed by Ayres 
have proved to be very serviceable means for accurately rating 
specimens of penmanship. After a careful study of the merits 
of the two scales and of the work that has been done with the 
Thorndike scale in a number of school systems, it was deter- 
mined to utilize the Thorndike scale in all of the measurements 
which are here presented. The method of administering the 
handwriting tests is given below. In this study, the effort is 
made also to determine quantitatively the amount a child can 
write. It is not fair to rate a class or a system on quality alone. 

THE TESTS IN HANDWRITING^^ 

1. Upon entering the classroom there was determined from 
the teacher what piece of poetry or prose containing thirty or 
more words had been memorized by the pupils. Often it was 
found that different groups knew different passages best. In 
that case each group was allowed to use what it knew best in 
the preliminary test. In Tests II, III and IV, it was found 
advisable to attempt to confine the writing to two different 
passages, preferably one, because of the difficulty in getting the 
passages on the board as noted below. 

2. Utilizing the regular monitors, one sheet of paper per 
pupil and pens in holders were distributed to the class. Care 
was taken to see that all were supplied with ink and blotters. 

3. The class was instructed to prepare this sheet by writing 
name, birthday, age, and sex as indicated under the Spelling 
Test. 

" Psychology and Pedagogy of Writing. 

^2 Manual of Penmanship and Guide to Rating, New Haven, 1912. 
For studies in the physiology of handwriting, the reader is referred to the 
work of Judd, Freeman and others. 

" A Scale for the Quality of Handwriting of School Children, Bulletin of 
the Russell Sage Foundation, 1912, No. 113. 

^* Handwriting, Teachers College Record, March, 1910. 

^5 In the Appendix the detailed directions are given so that any one who 
wishes to repeat these tests can reproduce the conditions exactly. 



Data Upon Which the Studies are Based 11 

4. Test I. Preliminary Test. The pupils were asked to write 
the first stanza of the passage selected over and over from memory 
in exactly two minutes. While the class was writing the names 
of any who did not remember the passage were recorded. At 
the end of that time, the papers were collected, fastened together, 
labelled as indicated for the other tests, and in addition they 
were marked, Preliminary, 120 seconds. 

5. Test II. Careful Writing Test. The teacher was asked to 
write the stanza on the board. If there were two or three 
groups, the investigator wrote one or more of the passages on 
the board, thus assisting the teacher and saving time. The 
pupils were then told that we were anxious to see how well they 
could write. They were told to write the first stanza over and 
over as carefully and as well as they could in the time allowed. 
They were told to look at the board if they forgot the passage. 
They were started on signal and allowed exactly four minutes. 
Papers were collected, labelled, and Careful, 240 seconds, was 
added. 

6. Test III. Writing Done At The Usual Rate Of Writing. 
The children were then told that the author wished to see how 
they wrote when they wrote about as rapidly as they ordinarily 
do. The same directions were given for the writing as indicated 
under (5) . They were started on signal and allowed exactly four 
minutes. Papers were collected and labelled as indicated above. 
Additional label. Ordinary, 240 seconds. 

7. Test IV. Speed Writing. ** Now let us see how you can 
write when you write very rapidly." Paper was distributed as 
before. ** When I say 'Go,' take your pens and write the stanza 
over and over again until I say * Stop ! ' Remember, write as 
rapidly as you can and still write well." The procedure was the 
same as in Test III and four minutes were allowed; the papers 
were labelled in addition. Speed, 240 seconds. 

ENGLISH COMPOSITION 

The most important studies of the achievement of pupils in 
the elementary school in English composition have been made 
by Rice, 16 Bliss, ^^ and Hillegas.^* These studies suggested 

16 Educational Research: The Results of a Test in Language. The Foruntf 
op. cit. 

" The Psychological Clinic, Vol. VI, No. 1, March 15, 1912, pp. 1-12. 
18 The Measurement of Quality in English Composition, op. cit. 



12 Variation in the Achievements of Pupils 

among other things the need of much work in the selection of 
a theme. After a large amount of preliminary experimental work 
with children's compositions and after a conference with a number 
of prominent teachers of English, the most helpful of whom was 
Professor Franklin T. Baker of Teachers College, it was decided 
that the subject best fitted for a test in English Composition is 
one which fulfills the following conditions: 

1. The subject must be within the range of the pupil. 

2. It must be a subject that will awaken his lively interest. 

3. It must be a subject that will challenge his best endeavor. 

In addition to the conferences with these teachers of English, 
the author examined with great care a dozen of the best language 
books and on the basis of this examination made out a list 
of subjects.^' After preliminary experimenting, the following 
was selected as the subject which most nearly conforms to the 
conditions noted above and fulfills the added requirement that 
fifth and seventh grade children are able to write freely upon it: 

"How I would spend one hundred dollars to please five persons 
who like different things." 

The results which have been obtained from the fifth and 
seventh grades are ample justification for its selection. The 
directions utilized in giving the composition test are as follows. 

THE METHOD OP ADMINISTERING THE COMPOSITION TEST 

One sheet of paper was distributed to each pupil. The pupils 
were asked to prepare the paper in the same manner as they 
had prepared their spelling papers. They were then directed to 
put their pens down and listen carefully to the following direc- 
tions : 

" To-day I am anxious to have you write a good story. 
I shall write a subject on the board and I want you to tell me 
the most interesting story that you can. After you begin (and 
do not begin until I say ' Go ') you are not to consult the dic- 
tionary or ask questions of anyone, not even your teacher. 
After I write the subject on the board you may ask me questions 
for a few minutes." 

Then the subject: ''How I would spend one hundred dollars 
to please five persons who like different things,'' was written on 

" More extended directions and the complete list of subjects are given in 
the Appendix. 



Data Upon Which the Studies are Based 13 

the board. Three to five minutes were allowed for questions 
which when answered gave a clear understanding of what was 
wanted. All others were eliminated. 

The class was then started and allowed to write twenty-two 
minutes. At the end of that time the writing was stopped 
and this direction given: '* You will now have a few minutes to 
look over your paper. Look through it carefully and make any 
corrections you wish without consulting anyone." 

Three minutes were allowed for this and then the papers 
were collected and labelled as indicated in the directions under 
" Spelling." 



TEST OF RANGE OF VOCABULARY^^ 

Range of Vocabulary has been studied at some length by 
Hall, 21 Whipple, 22 and others. The tests used in this study are 
designed to determine range of vocabulary, and when the equal- 
ity of the words has been determined, to be used as the basis for 
developing standardized methods for testing range of vocabu- 
lary of various kinds. It has not been possible to work out 
the equivalence of the words and accordingly only the gross 
scores are presented. 

TEST I 

These tests were administered as follows: The printed test 
papers for each of the tests were distributed face downward 
by the monitors. This direction was then given: "At the 
signal, * Go,' turn over your paper, read carefully the directions 
at the top of the sheet and then do as quickly as possible exactly 
what it says to do." 

The pupils were started on signal and allowed exactly three 
minutes. Names and dates of birth were then written upon 
the papers and the papers collected by the monitors. 

TEST II 

Directions and procedure identical with Test I. 



20 The author wishes to acknowledge his indebtedness to Professor E. L. 
Thorndike for the tests used in this section. 

21 Aspects of Child Life and Education, pp. 1-52. 

22 Manual of Mental and Physical Tests, 1910 edition, Chapter 12, with 
references. 



14 Variation in the Achievements of Pupils 

TEST III 

Directions and procedure identical with that in Tests I and 
II, except that five minutes was allowed. 

ARITHMETIC 

Even the casual reader of educational literature is impressed 

with the fact that an enormous amount of testing has been 

done in this field. The work of Rice, Stone, and Courtis is 

known to every one. 23 Aside from the commercial work of Mr. 

5. A. Courtis, a large number of publishing houses have recently 
issued new devices to aid in making a continuous test or survey 
of the arithmetic work of various grades of the elementary 
school. Many superintendents that are progressive have sought 
to improve these. For example, there was reported by Mr. 
J. T. Giles, 24 of Marion, Indiana, in 1911, a rather extensive 
series of experiments. A number of principals of the St. Louis 
schools have been at work for the last two years upon various 
forms of tests and methods of keeping records. Confronted 
with this mass of material it was difficult to decide what was 
best to use as a measure of arithmetical ability. 

After a careful comparison of the results and methods of de- 
riving tests, it was decided to select some of the Courtis Tests 
in view of the fact that 33,000 children had been given the 
Courtis Tests in New York City, during the progress of the New 
York School Inquiry. 2 & Tests 1 to 5 were rejected because it is 
felt that Tests 1 to 4 do not measure arithmetical ability in 
each of the four fundamental processes and that Test 5 meas- 
ures largely the speed at which figures can be written. Test 

6, Speed Reasoning, is fairly good. Courtis himself . reports 
that Test 8 is a very unsatisfactory test due to the fact that 
this test seems to involve difficulties which are inherent in the 
pupil's ability to read. 

Test No. 7, however, does not seem to be open to any of these 
objections. It is a graded list of problems in fundamental 
operations. Our effort has been to make as careful a standard 

2»0/?. cit. 

24 Report of the Department of Superintendence, 1912, St. Louis, Mo., p. 164. 

2"^ There is recognized much truth in the criticism of the method of deriving 
and applying standards used by Mr. Courtis (in this connection, see Bailey 
in Report of the Superintendent of Schools, City of New York, July 31, 
1913, p. 505 fl), yet for the reasons stated in this section, it was impossible 
to derive an arithmetic scale. 



Data Upon Which the Studies are Based 15 

measure as possible of the ability of the classes tested and since 
the Courtis tests are readily available, even if we deny the 
validity26 of Mr. Courtis's method of determining the standards 
of Test No. 7, we have at hand distributions of 27,171 individual 
scores of Test 7, made by children in the schools of New York 
City. These facts make it evident that we have a standard 
test and in addition distributions that will assist us in further 
standardization. Limits of time would not permit the making 
of an arithmetic scale before beginning this work which was 
the only other course open. The method of administering 
this test was the same as that recommended by Courtis." 

Section 2 
Other Data Collected at the Time the Tests Were 

Given 
Upon leaving the class room when the tests were given, 
there were recorded upon the envelope in which the papers 
were collected, the following facts: 

1. Name of city. 

2. Building. 

3. Grade. 

4. Teacher. 

5. Date of test. 

6. Exact time of day the test was given. 

For the purpose of determining for the various classes tested 
the class size for the preceding years, the average size of class 
in which the children had been taught was determined for the 
four preceding years, that due allowance might be made for 
the influence of class size in the grades preceding those in which 
the tests were given. The figure used in the column **size of 
class" is the average daily attendance. 

In order to determine the facts for each subject recorded in 
the columns '' hours in school per week," '' hours spent in home 
study per week," and " total cost of instruction per week," 
data were collected at the time of the visits to the classrooms 
and by letter from the teachers and supervisors and summar- 
ized on the following forms : 

2' See article by B. R. Buckingham, Journal of Educational Psychology ^ 
April, 1914. 

" Instruction book, 1913. 



16 



Variation in the Achievements of Pupils 

DAILY PROGRAM FOR EACH CLASS 
City School Grade Class 



Time 


Monday- 


Tuesday 


Wednesday 


Thursday 


Friday 



















































































































































Remarks: 



AMOUNT OF TIME REQUIRED FOR HOME STUDY IN EACH 
CLASS IN MINUTES PER WEEK 



City. 



. School 



Subject 


5B 


5Ai 


5 A2 


7Bx 


7B2 


7A 


Arithmetic 














Composition 














Spelling 














Penmanship 














Reading 















Note. — Fill in additional classes and give time in minutes per week for every 
class in which tests were given. 



Data Upon Which the Studies are Based 
DATA FOR COST OF TEACHING 



17 



Subject 


Name of 
Teacher 


Annual Salary 


Arithmetic 






Composition 






SpeUing 






Penmanship 






Reading 







City 

. Grade School 



1. In how many payments is the teacher's salary made ? 

2. How many weeks of school does each payment represent ? 

3. Please submit a complete calendar of your school year. 

For the purpose of studying the relationship between pro- 
motion rate and class size the promotion rate for at least one 
term and in some instances for two terms and the corresponding 
class size were tabulated for each of the systems. Similarly 
the salary of each teacher was tabulated by class sizes. De- 
tailed explanation of the relationship of these factors is made 
in Chapter V. 

Something should be said about the method used in rating 
teachers. Each superintendent was asked to rate his teachers 
by relative position. Most superintendents were unable to make 
more than five groups; some made six. The superintendent 
was asked to rate all of the teachers in the system. By the 
method commonly used for changing marks for relative posi- 
tion into units of amount, ^s the value of each superintendent's 
rating was found in terms of its A. D. The figure presented 
in the table represents the difference between these values and 
the average. The figures in bold face type represent distances 
below the average ; figures in other type represent distances above 
the average. Accordingly we are able to place the teachers in 
seven possible groups in terms of the ratings given in each 
system: At the average, first group above the average, second 
group above the average, third group above the average; first 
second and third groups below the average. 

2' For the technique used, see Mental and Social Measurements by Thorn- 
dike, 1913 edition, Chapter VIII. 



18 Variation in the Achievements of Pupils 

Section 3 

The Method of Scoring 

SPELLING 

In scoring the results in spelling, the twelve words given to 
each of the grades have been scored by the following method: 
The per cent of the pupils in the grade spelling each of the words 
correctly was determined. Since the words which were given are 
the words which are spelled correctly by approximately fifty 
per cent of the pupils in the grade on whose scale these words 
stand at the median, we have at once a measure of the status 
of a grade with reference to the grade standard in terms of the 
per cent of pupils who reach or exceed the median for the grade. 
As indicated in the table, the average of the per cents of the 
pupils spelling each of the standard words for a grade is taken 
as the status of the grade in spelling ability. The inter-grade 
comparisons^^ and inter-system comparisons are then made 
upon the basis of the per cent attained in terms of this standard. 

WRITING 

The method of scoring the handwriting is somewhat different 
from that followed in most studies. The handwriting has been 
scored both for quantity and for quality. 

To determine the qualitative score samples of the writing 
taken from the speed test have been scored by the Thorndike 
Scale. For the details of this, the reader is referred to Teachers 
College Record, March, 1910, and the reprinted form issued 
in 1912. A large number of samples taken at the ordinary 
rate of writing when scored, made no essential difference in the 
status of the grade, so it was decided to use the scores for quality 
based upon samples taken from the speed test.'" 

In order to determine the quantitative grade, after a careful 
survey of the records made in grades V and VII, it was evident 
that the only qualities worth considering are qualities 9 and 10. 
The next problem to decide was, ** What is the speed in letters 
per minute at which fifth grade children who are at median 

2»For details with regard to the measurement of spelling and the scales 
used, see Buckingham, op. cit. 

30 For the actual grading of the samples of handwriting and English com- 
position the form of scale now published by Teachers College was used. 



Data Upon Which the Studies are Based 19 

ability write respectively quality 9 and quality 10," and further, 
" What is the speed in letters per minute at which seventh grade 
children of median ability write qualities 9 and 10 ? " 

Upon distributing the scores in letters per minute written by 
fifths and sevenths at various speeds for qualities 9 and 10, the 
following standards were adopted as representing most nearly 
the median ability of fifth grades and seventh grades for the 
systems tested. No claim is made that this is a final standard. 
It has proved to be an exceedingly useful tentative standard 
and may be used in the derivation of finer standards. 

FIFTH GRADE. 

Quality 9 at 65 letters per minute. 
Quality 10 at 60 letters per minute. 

SEVENTH GRADE. 

Quality 9 at 95 letters per minute. 
Quality 10 at 85 letters per minute. 

The number of letters written per minute was determined by 
counting by means of a key sheet, which contained the passage 
written and the totals by line, stanza, and paragraph. The 
score was expressed as the rate in letters per minute. In the 
table of attainment presented in the succeeding chapter, the 
speed scores under each quality are in terms of the per cent 
of the total membership of each class that attains the speed 
standards for qualities 9 and 10 respectively for the particular 
grade considered. 

ENGLISH COMPOSITION 

The compositions were scored by the Hillegas Scale. In 
general the records for composition represent two independent 
scorings by this scale for each composition. For the details of 
the use of the scale, the reader is referred to the Measurement 
of Quality in English Composition by Young People, Teachers 
College Record, Vol. 13, No. 4, September, 1912. 

RANGE OF VOCABULARY 

The scores in this test were made upon the basis of the nimiber 
of words correctly interpreted, number of words omitted and 
ntimber of words wrongly interpreted. For the purposes of this 



20 Variation in the Achievements of Pupils 

study, the achievement is measured in terms of the number of 
words correctly interpreted in Test III. It was impossible to 
use the records from Tests I and II for the reason that they are 
too easy for the seventh grades, and hence the records are not 
comparable to the records of the fifth grades. This is not the 
case for Test III and accordingly this test was used throughout 
the study. When reference is made to the attainment of a 
grade, it is to be understood that this attainment is the median 
attainment for number of words correctly interpreted. 

ARITHMETIC 

For the test in arithmetic, as stated above, Test 7 of 
Series A, Courtis Tests in Arithmetic was used. The method 
of scoring adopted is that described by Mr. Courtis. The scores 
were made in Attempts and Rights. For the purposes of this 
study, scores are presented in terms of the number of problems 
solved correctly or in the language of Mr. Courtis, ** Rights." " 

METHODS OF COMPUTATION 

For the details of all methods of computation dealt with in the 
succeeding pages the reader is referred to Thorndike's ** Mental 
and Social Measurements," 1913 edition. The methods of com- 
putation referred to in this chapter are sufficiently simple to be 
clear from the brief description given. For such a rather in- 
tricate computation'2 as the determination of the per cent of 
fifth grade children who reach or exceed the median of seventh 
grade children in ability to spell sixth grade standard words, 
acquaintance with Chapter XIII of Thorndike" is desirable. 

»* Instructions for scoring. Special Graph Sheet, Test 7, Series A, 1914. 
'2 See Chapter III infra. 
^Wp. cit. 



CHAPTER III 

STANDARDS OF ACHIEVEMENT FOR FIFTH AND 
SEVENTH GRADE PUPILS 

The scores made by the seventeen hundred twenty fifth and 
seventh grade pupils ^ have been distributed by sexes and by 
half grades^ in order that we may determine so far as our data 
will permit the typical attainment for each half grade tested, 
and the amount of growth between grades five and seven and 
between half years of these grades. With the random sampling 
of pupils which has been explained in detail in Chapter II 
there are presented here a sufficient number of records to offer 
at least tentative standards. 

The data are presented in the tables which show (1) the 
complete distributions of the scores made by half years, and 
(2) the amount of overlapping^ by grades and half grades. So 
far as the form of distribution is concerned, it might be assumed 
throughout this study that ability in the subjects of spelling, 
handwriting, English composition, and arithmetic is distrib- 
uted according to the normal surface of frequency. The tables 
offer considerable evidence for this assumption. Where the 
distribution is cut off, it indicates the relative difficulty of the 
tests for the different grades, since the same test material was 
used throughout. Buckingham^ presents the argument for 
such a distribution of spelling abiHty, and since Buckingham's 
material is used in our spelling tests, this form of distribution 

^ Incomplete records of more than 200 children have led the author to pre- 
sent only 1,430 complete records for all the tests. 

2 In determining the half years in each of the grades, the first nineteen 
weeks of school is considered the first half year, and all time beyond the nine- 
teenth week is considered a part of the second half year. Thus, if tests were 
given some time in the first nineteen weeks of school, the scores are recorded 
as having been made by children in the first half year. 

3 In general this overlapping is the per cent of pupils, who, irrespective 
of sex, reach or exceed the median of the seventh grade, second half year. 
In addition certain facts of overlapping within the grades and by sexes have 
been calculated. 

* Op. cit. 

21 



22 Variation in the Achievements of Pupils 

has been assumed for spelling. The work of Ayres^ sug- 
gests that measures of the legibility of handwriting are dis- 
tributed approximately according to the normal surface of 
frequency. The distribution of scores of the Courtis test* 
indicates in general an approximation of the same form of 
distribution. For range of vocabulary the assumption of this 
form of distribution would not be fair because the relative 
difficulty of the words used in the tests has not yet been deter- 
mined. Accordingly the only course open is to compare roughly 
the gross attainment by grades and half grades. 

The imperfection of the scales^ used does not warrant us in 
making final assumptions in regard to the form of distribution. 
Accordingly, no assumption is made for the traits other than 
spelling. But, as will be shown later, since the size of group* 
in which these records were taken has not exerted an appre- 
ciable influence upon the scores, we are justified in gathering 
the records of all the children tested in the different half grades 
into tables such as these. The measures used, such as the gain 
by sexes upon the median of the lowest grade, and the per 
cent of pupils of a grade that reaches or exceeds the median 
attainment for pupils of a higher grade, is in nowise affected 
by the form of distribution. 

In examining the scores in the tables in this section, the 
student will note certain sex differences. These differences 
though large in several instances are not sufficient in amount 
for the subjects taken together to suggest separate provisions 
for the sexes. Until these are studied in connection with age 
differences, which was impossible in the limits of the present 
study, no conclusions of any validity can be advanced. But 

^ A Scale for Measuring the Quality of Handwriting of School Children. 

^ Final Report of the Committee on School Inquiry for New York City, 
1911-1913, Vol. I, pp. 385-546. Revised Graph Sheets for Test No. 7, 1914. 

' It should be stated very frankly that these tests do not enable us to 
make an accurate scale of ability in arithmetic, spelling, composition, or 
any of the other traits. All careful work in psychology shows that it is one 
thing to improve in ability from four to five on the Courtis scale and quite 
another thing to improve from eight to nine on the same scale. It is one 
thing to improve handwriting in quality from eight to nine on the Thorn- 
dike scale and a very different thing to improve handwriting from eleven 
to twelve on the same scale. 

8 The fact that the size of group has not exerted any influence upon the 
attainment is of great importance in considering the data for standardizing 
purposes. Since the data are not affected by the size of group in which 
the tests were made they gain added significance as tentative standards. 



Standards for Fifth and Seventh Grade Pupils 23 




Fig. 1. The amount of difference between grades V-B and VII-A when the 
per cent of pupils in the V-B grade reaching or exceeding the median 
of VII-A is 7.10. 




Fig. 2. The amoimt of difference between grades V-A and VII-A when the 
per cent of pupils in the V-A grade reaching or exceeding the median 
of VII-A is 12.5. 




Fig. 3. The amount of difference between grades V-A and VII-A when the 
oF VII^A ?s 19 ^^ *^^ ^'^ ^^^^^ reaching or exceeding the median 



24 Variation in the Achievements of Pupils 

we have here a body of data by sexes which is of value for 
comparative and standardizing purposes. 

By overlapping is meant the per cent of pupils in the fifth 
grades which reaches or exceeds the median attainment of the 
seventh grade, or the per cent of pupils in a lower fifth grade 
which reaches or exceeds the median of pupils in an upper fifth 
grade. An examination of the general tables reveals the fact that 
there is a large amount of overlapping in the grades. With over- 
lapping defined in this manner, it does not mean that where 
there is no overlapping portions of the surfaces of frequency 
do not enclose common areas. The central tendencies and 
variabilities show that they do. 

In the tables and diagrams which present the studies in 
overlapping, the reader will note that in each of the subjects 
the amounts of overlapping indicate the amount by which the 
half grades and full grades differ from each other, and as such 
are symptomatic of the amount of growth between these grades. 
To be most valuable, such amounts of growth should be checked 
by studies extending over several years, in order that we might 
have the data by which to standardize amounts of growth that 
should be required in the various grades. Such should be 
extended also to include all of the subjects. As stated in a pre- 
vious section, one of the most important contributions sought 
in this study is the derivation of a standardized method by 
which such studies may be carried on continuously in any 
school system. 

The striking thing in these results is that the half years of 
the seventh are very much closer together in all of the subjects 
than the half years of the fifth grade.' In arithmetic there 
are rather typical amounts of overlapping so far as the fifth 
grades are concerned. In English composition comparatively 
few students reach or exceed the median for the upper seventh 
grade, and here we find the seventh grades closer together than 
the fifths. 

In handwriting we have the very peculiar situation of very 
little overlapping. The central tendencies and variabilities are 

^ The amounts of overlapping were obtained by computing from the com- 
plete tables of distribution, the per cent of students by sexes, which reaches or 
exceeds the median selected as a standard. In general, for these per cents, the 
median of the upper seventh grade has been selected, although other signi- 
ficant amounts of overlapping are presented. 



Standards for Fifth and Seventh Grade Pupils 25 

so nearly equal that so far as these systems are concerned, we 
are forced to the conclusion that the tendency seems to be to 
have children write as early as the fifth grade, at a quality be- 
tween 9 and 10, and that not much higher attainment is re- 
quired in the other grades. As has been suggested above, it 
has not been possible to study the amounts of overlapping for 
range of vocabulary, as we know nothing about the relative 
difficulty of the words used. For the same reason, it is not 
possible to study the amount of overlapping for handwriting, 
measured quantitatively, because in the absence of experimental 
determinations we cannot state a standard which is compar- 
able with the other standards used in this study. Where the 
scores for quantity are used, they are to be considered as gross 
scores on the basis of the tentative standards suggested in 
Chapter II. 

What is presented in this and succeeding sections is offered 
with the hope that the method of investigation will prove 
suggestive, and that the various tables may be used as tenta- 
tive standards by which to work out more elaborate ones, and 
to determine what the amounts of overlapping in the various 
grades should be. In common with most of the recent studies 
of this character, the amounts of overlapping are exceedingly 
variable. This indicates, of course, that individual variation 
among pupils is certainly not provided for in any intelligent 
manner. The amounts of overlapping of the sexes while 
not suggesting the necessity for separate treatment, do at 
least suggest an important problem. These results are typical 
and represent typical ranges of attainment for American city 
systems, in so far as the s^^stems tested are typical of condi- 
tions in the United States. Every care has been taken to in- 
clude different population groups, different standards of teach- 
ing, and the like, as has been explained in detail in the previous 
section. 10 



10 Discussion of the tables and graphs has not been offered at length. The 
tables and illustrations summarize the results in form for convenient use. 
Complete tables of the results are not printed because the cost is prohibitive. 



26 



Variation in the Achievements 0} Pupils 



TABLE I 
ARITHMETIC— COURTIS TEST No. 7 



Scale 


Fifth 

Grade 

First Half 


Fifth 

Grade 

Second Half 


Seventh 

Grade 

First Half 


Seventh 

Grade 

Second Half 




B. 


G. 


Total 


B. 


G. 


Total 


B. 


G. 


Total 


B. 


G. 


Total 



1 

2 

3 

4 
5 

6 

7 
8 

9 
10 


6 
11 
15 

24 
15 
18 

6 
3 

1 

3 


2 

9 

17 

20 
17 
13 

5 
6 

4 

3 


8 
20 
32 

44 
32 
31 

11 
9 

5 

6 


19 
22 

25 

32 
38 
37 

31 
38 
29 

15 

5 
4 


15 
19 

27 

39 
35 
31 

18 
21 
18 

7 
.... 


34 
41 

52 

71 

73 
68 

49 
59 

47 

22 

1 


1 
1 
1 

7 

14 
13 

20 
19 
12 

8 

7 
7 

2 


"3 

2 

10 
3 

12 
10 
15 

12 
4 
6 

7 
3 
1 

; 


1 

1 
4 

9 

24 
16 

32 
29 

27 

20 
11 
13 

9 
3 
2 

1 
2 
1 


1 
4 
2 

16 
15 
14 

24 
32 
31 

26 

7 
12 

4 
6 
3 

3 
1 


3 
4 

7 

16 
13 
17 

24 
24 
20 

22 
13 
10 

2 
3 
3 

3 


4 
8 
9 

32 
28 
31 

48 
56 
51 

48 
20 


11 








22 


12 








6 


13 














9 


14 









1 




1 


1 
.... 


6 


15 








6 


16 
















1 


17 


















18 


















. . . . 




19 




















.... 
































Average. . 


3.98 


4.32 


4.15 


5.34 


4.65 


5.04 


7.15 


8.41 


7.80 


7.80 


7.37 


7.59 


A. D 


1.51 


1.52 


1.65 


2.24 


1.99 


2.08 


2.15 


2.48 


2.33 


2.33 


2.46 


2.40 



Standards for Fifth and Seventh Grade Pupils 27 

vSuMMARY OF RESULTS BY GrADES, HaLF GrADES AND SeX FOR 

Each of the Tests. Amounts of Growth by 
Half Grades and Sex 

ARITHMETIC 

In arithmetic, measured by results obtained in Test No. 7 
of the Courtis tests, the girls are superior to the boys in the 
first half of the fifth year and the first half of the seventh year, 
but the boys are superior in the second half of each of these 
grades by the amounts which follow. Measured by the per 
cent of all pupils in the half grades that reaches or exceeds 
the median of Grade VI I- A the amounts are as follows : 

Grade V-B Grade V-A Grade VII-B 

7.1% 19.0% 48.0% 

If we consider the influence of sex the following per cents 
of boys reach or exceed the median for girls in each half grade: 

Grade V-B Grade V-A Grade VII-B Grade VII-A 
36.3% 60.5% 28.3% 55.7% 

From an examination of the table of results, it is seen that 
there is growth in median attainment throughout the grades 
for boys. For girls there is little growth between half years of 
grade five and the girls of the first half of grade seven are 
superior to the girls of the second half of this grade. A careful 
examination of the sources of the data indicates that this supe- 
riority is not the result of a selection from the best systems. ^^ 
On the contrary, what would be regarded as the poorest school 
population is included in this set of records. In the fifth grade, 
the boys show a growth on their median ability for the first 

" In general the standards for the testing of work in the various classes 
examined are not radically different. The classes of System D are examined 
more particularly than those of other systems to determine the amount of 
growth in attainment in a certain period. It is almost impossible to estimate 
the amount of influence which this requirement would have as compared 
with the amount of influence which the usual requirement that children meet 
the standards of the tests set by the supervisory officers at various intervals 
exerts. From a careful discussion of this subject with the supervisory officers 
in the various systems, the writer has been unable to determine any differ- 
ence in the effect upon teachers or the attainment of classes. The results 
obtained in the classes in System D do not indicate the operation of a superior 
force. Since all of the systems offer examinations set by the supervisory 
force, the amount of influence which the particular "system" of examina- 
tions exerts may be regarded as negligible so far as the results reported in 
this study are concerned. 



28 Variation in the Achievements of Pupils 



ZO 



/S 



iO 



Jl 



^ 



Z 3 



5 6 7 Q 9/0 



II 



Fig. 4. Typical Distribution. Arithmetic. Grade V-B (Boys and 
Girls). 

The frequencies are expressed as per cents of the pupils in this grade; 
7.10 per cent reaches or exceeds the median for grade VII-A. 

half year of the grade, of 1.36 or 34.2 per cent. In the seventh 
grade they show a gain of .65 on their median abiHty or 9.9 
per cent. The differences for girls are as noted above. For 
the sexes taken together, the gain in the second half of the 
fifth year on median attainment of the first half year is .89 
or 21.4 per cent. For boys and girls throughout the grades, 
the gains on their median attainment for the first half year 
of the fifth grade are shown in the following table: 

ARITHMETIC 



Grade 


Boys 


Girls 


Both Sexes 


Attain- 
ment 


Gain 


Attain- 
ment 


Gain 


Attain- 
ment 


Gain 


Grade V-B 

Grade V-A 

Grade VII-B 

Grade VII-A 


3.98 
5.34 
7.15 
7.80 


i:36 

3.17 
3.82 


4.32 
4.65 
8.41 

7.37 


■.33 
4.09 
3.05 


4.15 
5.04 
7.80 
7.59 


'.'89 
3.65 
3.44 



Standards for Fifth and Seventh Grade Pupils 



29 



TABLE II 
ENGLISH COMPOSITION 



Hillegas 
Scale 


Fifth Grade 
First Half 


Fifth Grade 
Second Half 


Seventh Grade 
First Half 


Seventh Grade 
Second Half 


B. 


G. 


Total 


B. 


G. 


Total 


B. 


G. 


Total 


B. 


G. 


Total 





37 
11 
43 

45 
75 
34 

24 
4 
2 

3 


22 
2 

37 

40 
81 

45 

23 

20 

5 

1 


59 
13 
80 

85 

156 

79 

47 

24 

7 

4 








2 


1 


3 








30 


6 
10 

25 
27 
22 

25 
13 


1 
8 

15 
6 
3 

11 
5 
6 


7 
18 

40 
33 
25 

36 

18 

6 








60 
120 


i 

6 
41 
76 

45 
46 
17 

8 
11 


"'35' 
39 

46 
47 
39 

25 
15 


1 

6 

76 

115 

91 
93 
56 

33 
26 


1 




1 


183 
222 

260 
315 
369 

422 


3 
24 

15 
7 
4 

2 

7 
3 

2 

1 


"9" 

5 
5 
1 

7 
9 

7 

1 

'"i" 


3 
33 

20 

12 

5 

9 


474 








16 


530 














10 


585 




1 


1 










1 


1 


3 


630 










1 


675 














1 




1 


1 


















Median 


183.5 


201.3 


218.5 


217.7 


209.0 


215.0 


262.5 


319.5 


290.8 


285.7 


444.3 


319.5 


Q 


65.8 


56.95 


61.57 


56.5 


85.6 


64.6 


54.5 


75.8 


64.5 


74.61 


115.63 


116.27 



The growths through the grades by sexes and by pupils, 
irrespective of sex, are shown in the table of overlapping. These 
facts are also illustrated in the diagrams. These amounts of 
growth may be taken as typical for cities similar to the ones 
tested. The very striking thing, of course, is the fact that the 
half years of the seventh grade are practically together, whereas 
there are distinct differences between half years of the fifth 
grade, and between the fifth and seventh grades. 

These amounts of growth would be further illuminated by a 
study of growths within the different grades over various periods 
of time. It is impossible to present measures of this kind 
within the limits of the present study, although these data are 
being collected for a large number of the same children whose 
records are included in this report. This matter has been 
studied somewhat by Courtisi^ and Rail. 13 The median attain- 
ment from tests made in New York City in 1912 by Mr. Cour- 
tis was, for 5836 children of the fifth grade 5.8, and for 4771 
seventh grade children 8.5. The amount of growth measured 



12 First and Second Annual Accountings. 

13 School Review Monograph, No. 3, Feb., 1913, pp. 36-45. 



30 



Variation in the Achievements of Pupils 



by median attainment is 1.7 or 30 per cent.^* In the recent 
publication of diagrams based upon the scores of 2000 classes 
in the cities of New York, Boston, Detroit, and similar cities 
in fifteen states, ^^ the average attainment for grade five is given 
as 4.7 and for grade seven as 7.7. The amount of difference 
in average attainment is three " rights." These amounts, 
however, are not as valuable as the records in this section, 
because the medians represent a figure taken from the scores 
of children indiscriminately mixed as to sex, age, and half grades. 



COMPOSITION 

The tabulated results in Table II show growth throughout 
the half years for boys and for girls. The same is true for the 
sexes considered together, although there is practically no 
difference between the attainment of the first and second half 
years of the^ seventh grade. The amounts of growth in terms 
of the median for the first half of the fifth grade are as follows: 

ENGLISH COMPOSITION 



Grade 


Boys 


Girls 


Both Sexes 


Attain- 
ment 


Gain 


Attain- 
ment 


Gain 


Attain- 
ment 


Gain 


Grade V-B 

Grade V-A 

Grade VII-B 

Grade VII-A 


183.5 
217.7 
262.5 
285.7 


*34!2 

79.0 

102.2 


201.3 
209.0 
319.5 

444.3 


'"7!7 
118.2 
243.0 


218.5 
215.0 
290.8 
319.5 


—3.56 

72.3 

101.0 



Measured by the per cent of all pupils in the half grades 

that reaches or exceeds the median attainment of Grade VII-A, 

the amounts of overlapping are as follows : 

Grade V-B Grade V-A Grade VII-B 

6.1% 12.8% 40.3% 

Sex differences are prominent in this trait also. The per 

cents of boys reaching or exceeding the median attainment for 

girls in each half grade are as follows: 

Grade V-B Grade V-A Grade VII-B Grade VII-A 

38.4 % 54.0% 31.7% 21.7% 

" Final Report of the Committee on School Inquiry for New York City, 
1911-1913, Vd. I, p. 434. 
15 Revised Graph Sheet for Test No. 7, Series A, 1914. 



Standards for Fifth and Seventh Grade Pupils 
SPELLING 



31 



The scores made for the words by grade gain added interest 
if compared with the findings of Dr. Buckingham. For the 
benefit of the reader, I quote the following results from Buck- 
inghami^: 



Word 


Lower Grade 

% 


At Grade 

% 


Higher Grade 

% 


Fourth Grade 

Wear 


35 
32 

45 

37.2 
24.7 
39 
40 

40 
40 
37 

37.6 
42.9 
33.6 
40.2 

46.3 
91 

43.6 

44.4 


49 

52 
52 
48.4 

49.7 
49.1 
50 
50 

52 
49 
46 
53 

52 

51.8 
47.7 
47.1 

56.1 
97.1 
50.4 
49.6 


61 


Button 


61 


Touch 


60 


Surface 


79.1 


Fifth Grade 
Believe 


64 4 


Loose 


45 2 


Circus 

Carriage 


72 
67 


Sixth Grade 

Saucy 


71 


Whistling 

Beginning 

Succeed 


68.7 
66 
70 8 


Seventh Grade 

Ascending 

Slipped 

Imagine 


55.7 
70.9 
66.4 


Character 

Eighth Grade 

Peculiar 


78.7 


Mixture 




Intelligent 

Occasion 


.... 







We find the girls superior to the boys in all of the grades, 

although the differences as has been suggested before, are not 

sufficiently significant to suggest different provisions for the 

sexes. There is a rather uniform growth throughout the grades 

for boys, and a somewhat less uniform growth for girls. The 

girls in the second half of the fifth grade are practically equal 

to the boys, and but slightly inferior to the girls of the first 

half of the seventh grade. For the sexes considered together, 

there is a growth throughout the grades. In computing the 

amount of growth from Grade V to Grade VII it would be 

possible and valid to compute the amount of overlapping of 

i^Spelling Ability, Its Measurement and Distribution, pp. 14-15, 78-79 
104-105. 



32 



Variation in the Achievements of Pupils 





W 




> 




H-l 




CO 




P 




hJ 




O 




^ 




l-H 


o 


d 


;3 


o 




< 


CO 


CO 





Per 

Cent 
Right 


On CS t^ !>• 


vOI>- VO Tti 


IOCS'* vO 




1 


t^ SO lO t^ 


00 Ot^io 


dvdood 

so Ttl CO Tfl 




o 


|2 


ONCMO'* 
CM T-l 0\ CO 


'xft rO Csl 00 

Ot^OON 

1— ( T-i 


i>. CO 00 fO 
O OOsOt^ 

T— 1 







Per 

Cent 
Right 


SOrHfOVO 


SO SO tH CO 


sOfOOro 




m 

i 


■^ tH lO OS 

oot-iooo 


tH csl -^ so 

CO lO t^ !>• 


00 toioio 


OO 


1- 


7— 1 r^ ■<-« T:f< 
CO CSCNCO 


■--1 01>- OS 
COCN CNCN 


T-l -.-1 OS tH 
CO(>l^CS 


CO 









lO CS CS Os 



lO CN OS SO 



CS OO CO Os 
lO CO lO •^ 



t^ sOrOr^t 



r:}H ri< lOi>. 
lO -^ CO CO 



SO CM OS CM 
J^* so -^ »0 



m 






CD 4J 



CM CN COt- 
OO lO OO -^ 
CO CO CN CO 



lO OS O lO 
t^ Os lO OS 
CN CN CN •■-I 



SO O CO OS 
CO CN CO CO 



▼H CN OS CO 
CN ••-H ^ CN 



o 



4^ 4-> 



CN lO CN lO 

•rH OS SO OS 
CN T-t r-l tH 



CO Ot^ O 
sot— '* CN 






;3 o p! 
WHco 



> 

CD m 

'^ O 

CD O 



(D 



m^oo 



t-lOCNt- 



cot^pqco 



Standards for Fifth and Seventh Grade Pupils 



33 



> 

CO 

3 

.5? O 





Per 

Cent 
Right 


OOOOOOO 


CD tH CO CO 


00lOt>- tH 




1 


On -rH lO On 


OO t>- NO NO 


lONO •r-l VO 
NO ONlOlO 






1^ 


T-( tH lO "-H 
ON OOt-- ON 


lO NO ON On 
On 00 t^t^ 


lOOON^ 

t^ O lO NO 





o 









t^ On CO CM 



t^ CN tH CO 



rt< tH ^ 00 



pq 






NO On Jr^ NO 



t^lO CS -rH 



ffi 



fe 






tH IT) CO 00 



00 NO t^ NO 
CN OO CS •r-l 

CO CS CO CO 



NO rt< 00 ON 



J>- to On CO 
CS NO CO On 
CS CM CNl cs 



to NO On t^ 



NOtH T^W 

On NO lO ON 
CS CO CNJ <M 



o 



III 



|1i 



O.J2.J:! o 



O Oh $3 $S 

<c/2>5o 



»H (U (U g 









34 



Variation in the Achievements 6f Pupils 



the grades in terms of the four words common to the two lists 
(i.e., sixth grade standard words spelled by 50 per cent of the 
pupils) by reference to the normal surface of frequency. Or 
the amounts of growth from grade to grade may be computed 
from Buckingham's scale. The latter method is more precise 
because it enables us to use all of the words in each list and 
has been adopted. 



^52? 4?^ SP i/O (>30 ifO 6p He 



730 7S0 770 



tio iio tso 



m m fjo fsv 



r 



—\ : 



I 



Fig. 5 



The method is illustrated in Figure 5. The figures above 
the line represent spelling ability measured from zero. The 
method briefly is this: Four words were selected from the 
list given to Grade VI I- A, which are spelled roughly by 69 
per cent of the pupils and their position on the scale marked. 
Using this figure as the standard, the four words spelled by 
this per cent of pupils were selected from the list for each half 
grade and their position marked on the scale. Allowance 
should be made for the fact that the various words are not 
spelled by exactly 69 per cent of the pupils in the various 
grades. The correction is small in most instances and would 
not affect the inferences which are drawn in this section, so no 
elaborate method of rescaling has been adopted in the diagram. 

The writer has also scaled carefully each of the twelve words 
for each half grade by precisely the same method which Buck- 
ingham used in the construction of his scales. (See especially 
pages 61 and 116 of '' Spelling Ability," op. cit.) This does not 
modify any conclusions with respect to the amount of growth 
between grades five and seven that may be drawn from the 
relative position of the words as they stand upon Buckingham's 
scale. (The diagram represents the position as determined by 



Standards for Fifth and Seventh Grade Pupils 



35 



Buckingham, not the position which would be assigned by 
sixty-nine per cent.) The amount of growth from grade five 
to grade seven, giving weights of five and two respectively to 
the records of the first and second half years is 1.007 P. E. or 
roughly about 100 units on Buckingham's scale. The amounts 
of growth for the separate grades are as follows: Grade V-B 
to Grade V-A, forty-four units; Grade VII-B to Grade VII-A, 
fifty-two units. 

WRITING 
It is impossible to present standards or amounts of growth 
for these grades in handwriting, either for quality or quantity 
which may be taken as final. However, we do have growth 
from grade to grade with some peculiar deviations if we con- 
sider the sexes separately. For quality the gains are shown 

below : 

HANDWRITING 



Grade 


Boys 


Girls 


Both Sexes 


Attain- 
ment 


Gain 

Amt. 


Attain- 
ment 


Gain 

Amt. 


Attain- 
ment 


Gain 

Amt. 


Grade V-B 

Grade V-A 

Grade VII-B 

Grade VII-A 


9.40 

9.95 

9.85 

10.50 


'."55 

.45 

1.10 


9.90 
10.67 
10.56 
11.42 


".■77 

.66 

1.52 


9.62 
10.15 
10.25 
10.77 


■.'53 

.63 

1.15 



As explained in Chapter II, the distribution of the various 
speeds for qualities nine and ten for the various half grades shows 
that the only tentative standards that could be considered are 
as follows: 
Grade five : 

Quality nine at 65 letters per minute. 
Quality ten at 60 letters per minute. 
Grade seven : 

Quality nine at 95 letters per minute. 
Quality ten at 85 letters per minute. 

These may not be regarded as more than tentative standards 
until experimental determinations are made of the growth in 
power to write at various speeds and qualities as children pro- 
gress through the grades. In the absence of this evidence they 
are serviceable in that they give us a rough index of the growth 
in speed at the same quality. 



36 Variation in the Achievements of Pupils 

TABLE IV. RANGE OF VOCABULARY. TEST III 





Fifth 




Fifth 




Seventh 


Seventh 


No. of 


Grade 


Grade 


Grade 


Grade 


Words 


First Half 


Second Half 


First Half 


Second Half 


Correctly- 
















Recog- 






























nized 


B. 


G. 


Total 


B. 


G. 


Total 


B. 


G. 


Total 


B. 


G. 


Total 


0- 4 


6 


4 


10 


17 


4 


21 


5 


1 


6 


3 





3 


5- 9 


5 


3 


8 


9 


4 


13 


9 





9 


1 





1 


10-14 


8 


2 


10 


4 


6 


10 


4 





4 


1 





1 


15-19 


19 


4 


23 


15 


5 


20 


1 





1 


1 





1 


20-24 


10 


14 


24 


17 


10 


27 


2 


1 


3 











25-29 


16 


14 


30 


28 


8 


36 


2 





2 


4 


1 


5 


30-34 


17 


21 


38 


21 


18 


39 


5 


3 


8 


7 


1 


8 


35-39 


18 


24 


42 


17 


22 


39 


4 


3 


7 


3 


3 


6 


40-44 


11 


26 


37 


24 


15 


39 


4 


7 


11 


4 


2 


6 


45-49 


13 


14 


27 


28 


20 


48 


11 


4 


15 


8 


10 


18 


50-54 


8 


12 


20 


25 


20 


45 


8 


7 


15 


16 


17 


33 


55-59 


6 


14 


20 


18 


20 


38 


17 


13 


30 


19 


28 


47 


60-64 


9 


6 


15 


17 


8 


25 


25 


19 


44 


58 


58 


116 


65-69 


3 





3 


2 


6 


8 


13 


11 


24 


67 


50 


117 


70-71 


2 





2 











1 


1 


2 


23 


16 


39 


Median. . . 


33.5 


38.5 


36.4 


38.3 


42.3 


40.0 


55.3 


58.9 


56.7 


63.6 


62.8 


63.1 



TABLE V. HANDWRITING 



Thorndike 
Scale 


Fifth Grade 
First Half 


Fifth Grade 
Second Half 


Seventh Grade 
First Half 


Seventh Grade 
Second Half 


B. 


G. 


Total 


B. 


G. 


Total 


B. 


G. 


Total 


B- 


G. 


Total 


4 


1 

4 
4 


1 


1 
5 
5 




















5 




















6 








































7 


6 

60 

121 


"se" 

106 


6 

96 

227 


1 

5 

71 


■■23' 


1 

5 

94 


4 

24 

111 


35 


4 

28 

146 








8 
9 


1 
27 


"io' 


1 
37 


10 
11 
12 


40 
5 
1 


103 
9 

4 


143 

14 

5 


48 
12 

7 


21 

13 

5 


69 
25 
12 


78 

18 

5 


122 

40 
8 


200 
58 
13 


36 

15 

5 


11 


48 
34 
16 


13 
14 
15 


1 

1 


3 

1 
1 


4 
2 
1 


2 

1 
1 


6 

1 
2 


8 
2 
3 


2 

1 


4 

1 


6 
2 


5 


4 
1 

1 


9 
1 
1 














16 




1 


1 




1 

1 


1 

1 








1 


1 


2 


17 
































Median 


9.4 


9.9 


9.62 


9.95 


10.67 


10.15 


9.85 


10.56 


10.25 


10.50 


11.4 


10.77 


Q 


.575 


.64 


.68 


.637 


.97 


.837 


.63 


.45 


.63 


.72 


.95 


.88 









Standards for Fifth and Seventh Grade Pupils 



37 



RANGE OF VOCABULARY^'' 

For the reasons explained at length in the preceding sections, 
it is impossible to present measurements of growth, either by 
per cent of improvement on the median scores, or by the 
amount of overlapping, because of the inequality of the words 
used in the tests. The complete tabulations of the achievements 
of the pupils in this test by grades and sexes, furnishes a con- 
venient table of reference for the use of those investigators who 
desire to repeat the test, and the following summary gives in 
convenient form an index of the growth in range of vocabulary 
from grade to grade if it is interpreted with the caution sug- 
gested above. 

RANGE OF VOCABULARY 



Grade 


Boys 


Girls 


Both Sexes 


Attain- 
ment 


Gain 

Amt. 


Attain- 
ment 


Gain 

Amt. 


Attain- 
ment 


Gain 

Amt. 


Grade V-B 

Grade V-A 

Grade VII-B 

Grade VII- A 


33.50 
38.30 
55.30 
63.60 


'4:80 
21.80 
30.10 


38.50 
42.30 
58.90 
62.80 


20.40 
24.30 


36.40 
40.00 
56.70 
63.10 


'3.60 
20.30 
26.70 



" It should be stated frankly that the author recognizes the fact that 
possibly the best method of determining range of vocabulary has not been 
used. If we wish to obtain the true range it could probably be done better 
by giving the student all the time he needs to mark the words he knows. On 
the other hand, if we wish to obtain his range in a definite time it would be 
advisable to set a time limit. However, it may be said in defense of the 
"mixed method" used that fairly good seventh grade pupils were able to 
recognize in the time allotted, five minutes, all of the words which they 
know in Test III. 



CHAPTER IV 

ATTAINMENT IN CLASSES 

Possible Uses of the Scores of Attainment and 
Related Facts 

In this chapter there are presented complete tables which 
summarize the achievements of all of the fifth and seventh grade 
pupils by classes. Measurements of attainment and variability 
are given for each class. Other data presented give us a sam- 
pling of the following facts : Size of class, size of class in which 
the children have been taught for four years previous to the cur- 
rent school year, the annual salary of each teacher, the number of 
hours per week devoted to each subject in school, the number 
of hours per week devoted to each subject in home study, the 
total cost of instruction per week in each subject, and the date 
of the test. 

The sufficiency of the data has been discussed in detail in 
Chapter II. So far as the grades and systems tested are typical 
of American cities, in addition to giving data on size of class in 
relation to these factors, the table furnishes typical limits of 
attainment for the various subjects tested. ^ It also offers in 
the form of a summarized random sampling from many classes, 
suggestive limits in time allotment for these subjects^ in school 
and requirements for home study. Other facts given in the 
table may be utilized in making detailed analytical comparisons 
as has been done in the succeeding pages only for attainment, 
variability and amounts of overlapping. 

In Chapter V is given a table of overlapping. This table has 
been computed somewhat more in detail than the ones given in 
Chapter III for all the scores taken together. Overlapping by 

1 With the exception of English composition. By utilizing more judgments 
than it was possible to do in the present study, the gross attainment would 
be slightly higher but the relationships among the grades would be unchanged. 

2 Cf. studies of time allotment by Stone in Arithmetical Abihties, Payne in 
Public Elementary School Curricula, Elson in N. E. A. Report, 1911, op. cit. 



Attainment in Classes 39 

grades and half grades, and by small and large classes, is given 
for arithmetic, composition, and spelling. 

In the following discussion, attainment of a grade is to be 
understood as the median attainment for the grade. The 
variation, unless otherwise stated, is expressed in terms of Q. 
Careful analysis of the scores for attainment in the various 
traits and the amounts of variability in Table VI does not 
reveal any correlation between these facts and the size of group 
in which the measurements were taken. But the data exhibit 
over and over the influence of growth in ability and indicate 
the value of the tests for measuring amounts of growth. 

Detailed study of the table shows that the differences in 
amount in all the traits are closely related to amounts of 
growth. Such variations as appear in the scores that are taken 
in the same week of school in the various systems are such as 
are common in measurements with relatively rough scales of 
school traits such as these. Let us make a sample analysis of 
the scores of the seventh grade in arithmetic for a number of 
systems to illustrate the point. 

In System D, in the second week of school we have a score of 
7.9 in a class of twenty-six; a score of 6.4 in a class of twenty- 
nine; a score of 8.1 in a class of thirty-two, and a score of 8.4 
in a class of thirty-four. The highest scores appear in the 
classes above thirty. The next to the highest score is found In 
a class of twenty-six and the lowest score in a class of twenty- 
nine. Again, there seems to be no correlation between the size 
of class and the attainment. In System E, classes of thirty- 
three and twenty-six, measured in the twenty-fifth week of 
school, make respectively scores of 8.65 and 9.29; the class of 
twenty-eight tested in the sixth week of school makes a score 
of 7.54; the better score is made in the smaller class. However, 
the difference between these scores is not nearly as great as 
the smallest difference between the class half a year behind 
these. This evidence of nineteen weeks of growth, ^ more potent 
than any influence of class size, is abundantly confirmed by 
the attainments in English composition, writing measured for 
quality, spelling and range of vocabulary. In System F we do 
do not hav e any evidence of the influence of class size or any 

^ These amounts of growth are comparable to those cited by Rail, School 
Review Monograph, No. 3, Feb., 1913. See also Courtis Graph Sheets for 
Test, No. 7, 1914. 



40 Variation in the Achievements of Pupils 

significant measures of growth. There are other contributing 
factors which further study should take into account.-* 

In System G, we have a class of thirty-nine in the ninth week 
of school making a score of 6.91 and a class of thirty-two in the 
twenty-eighth week of school making a score 36.5 per cent 
higher. In the light of the evidence of growth cited above 
and the inter-system comparisons of growth, it is not conceiv- 
able that the reduction in membership of the class is sufficient 
to account for the larger score. Nineteen weeks of growth of 
the children is a far more logical and scientific explanation in 
the light of all of the facts cited in the discussions of this and 
succeeding sections. 

The author has patiently made the same analysis for every 
trait and its variability for every class. The same evidence of 
growth and close correlation with attainment is present. Let 
us repeat: These classes are a wide selection from many more 
classes and care has been taken to get the smallest, middle 
sized, and largest classes in the fifth and seventh grades of the 
systems measured. Consequently the potency of the factors 
of growth, size of group, and the like readily becomes evident. 

* The most probable cause here is the character of the population. 



if 



Attainment in Classes 



41 





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T-|^^,-|^^TH..-H.p-l,-|T-|.r-<^T-l,-I^^O«0»0 


3aaAV ^3d[ 

NOIXDnHXSNI KO XSOD TVXOX 


C<IOO.rHOO'*lO\OrJH'.-lOO\0000\'5i<"^CNOO'r-t 
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saaAV Haj Aanxs anon sHnoH 


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u-)CSl\OvOOOvOOvO'<*t^\OCNtotoiOvOfO(NCSO 


CM .^ rH ^ T^ ^ CS ^ esq ^ ^ O 


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to 

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aavHO XV 


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t~-lOlOOCNCNtOlOt^OlOCSlOlOCSlOU-)l>.00 

i0iOT}<^0^0i0»Ot>-OO-^Ot^iOV0iOt^t>-C\C0 


aavHo 


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Hanovax 


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AXID 


<^<i:<<<;<;<:<<<;pqpqFqpqOUUQQQ 



42 



Variation in the Achievements of Pupils 





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saaM saj 
NOixDnnxsNi ao xsod tvxox 


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HaaM «a£ Aanxs anoH shiioh 


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CNOCMCOCOCSVOOOVOONCSIOU^CSCSOOOOCOCO 


■.-1 CS T-l ■.-1 ^ tH tH tH •.-H tH ^ ,-1 CS CS •r-l rH ^^ 




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co-<:t<Ou-)oO'0'*iO»Oi:^vOvOcoc<H>.vO'*ThiiOvO 


aavso XV 


OOOOOOcovOT^OrtHvOC^OOOiOiOrf^OCO 


vOiOOiOl>.Oas00-.-i^'^T-l<fH0NT-iCNV0t^<MC0 
iOsO\OCOl>>vO'5ti'*vOl>-t^OOiOCOOOMOiO-r}<lOt^ 


aavHO HaMOT 


OOOOOO'OiO0\OOt-t--r-H>.t^O0N00CS 


vOr-t\OT-400a\OO\O0N0NO0NOr<i\O00t^T:t<0N 
>OvOiOiOvO>Ot^vo^t^t— r-io^ooot^t^voiovo 


•SHA ^ SSV13 ao azis aovnaAV 


rJ^T*^^^^r-^l^^r^^r^O^C^O^OOcocoOOOOOO 
cocOcococOCOCOCOCOCSCSCS|-<;t<-<*Tj<Tj<-rt<'*cocO 


ssviD ao azis 


00v0v00NCN-^Ov00000C0\OiO00TtH>.000N0sCS 
CNCOCS^cscocOrt^cocOCS^coc^l'*rl^cococOCOCOCO 


AHVIVS TVriNNV 


OOOOOiOOOOOOOOOOOOOOO 

lOOlOlOOt-OOOlOOO'<-HCM-<*CMOCNrt<CS 

CX300000NO0N000000t^0000'.-lO00>*lOt^Ti<Cl0 
tH tHtHtH'tHtH'.-H^-H 


aavHO 


pq <^ < m <^ <J pq < pq <j < < pq <^ 


ONixva 


<N<S<S<S(NOOVO<5VOVOSO^I>COCOCOOOOO 

,.Hi-J»Hi-JiHOO'rHTHTH.^.r-IOOO^OOOCOI>COCO 


HaHDvax 


*HCMC0'^iOMDt^00ONOTHC<|C0Tt<tOvOt^000\O 
CSCS|(MCsICNCSCSCSCNCOCOCOCOCOCOCOCOCOC0t}< 




AXID 


QQQQQQWWP^WWWfofefefeOOOO 



Attainment in Classes 



43 






HasAv Haj NOix 

OnaXSMI AO XSOD TVXOX 



aaaM. 
Had Aaaxs awoH shhoh 



xaaM. 

Had aOOHDS NI SHXIOH 



t-HOOTHOvcOTHt^OOOOsOOOOOiO-^ 
ONOOi-ir^'^tO'«-n:^t^csvOCOooiooouot^ 



CO O O O Ol>- fO O Ot^ O e01>- OO 
000«OOO^fOOOvOOOOvO»000»0 

O OO fO O O O ^CSOOro 



t^ fO O O fO 00 CO fO 00 CD CM CD 00 to 00 O 
..-It^-i-Hi-lOOiOCSCOCOCSfOONCOCSlOOT-t 

•<!j<(N-«;t*Tl<T^CSrOfOfOPOtococOfOiO'*fO 



AxmaviHVA 



XNaWNIVXXV 



cs fOioroio 



lO-^iOt^iOrtiONOiOfOt^ 



xsax ao saaAi 



xaaAV Had noix 
onHxsNi ao xsod tvxox 



HaaAV 
Had Aanxs awoH snaoH 



3aaAi 

Had aOOHDS NI SHIIOH 



AxmaviHVA 



eMCMr<i(Mr<icMcscscs?M(Mcsp<icscsi<Mr^ 



T-l CS tH T-H 



O O O O O Or~ «ot^ O O fO 

OOOOOiOvOt-^iOOOiOOOOOO 

ooooo "oo'ooo 



CNCS<MCSCSCO'>-4t-(T-Hi-<CSCS'r-lT-lCSCO'«-( 



oooocsiorsivo-rj^oOMDooiOTMOO'-iio 

i-ioocN'^ror-r^ooOt^»ocsooONONO'0 
VO-^cOSOlOCNOOOiOCOCST-lcOiOt^CS-^ 



XNaHNIVXXV 



fOCOt-^000'>-H'-iiOVOvOt^O-^0»OONO 

P0OrH00i>.0\00t^rs0NVOu-)t-.Or<l-^^ 
i-(Of0C000J>-O000NJ>-l>-'^t0OO'r-irt( 
<NCNCN'^THi-(COCNCOCOTHCNfOfOCNCS<M 



aavHO 



toiOtoio»OtOI>.t^t^t^iOiOt^t^iO»Ot^ 



HaHDvax 



T-tCSrO'^i001>.000\Oi-l(MCO'^tOV01>. 



AXID 



<;<<<<;<<<i^<^<pqpqpqpqOOCJ 






44 



Variation in the Achievements of Pupils 



xsax do HaaM 



3aaM ^aj noix 
onsxsNi ao xsod tvxox 



3aaAV 
Had Aanxs anoH s^noH 



3aaAV 
^aj qooHDs Ni s^noH 



AxniaviHVA 



CSCSCNCSCSCSCNCNCNVOlOloOlOlLOOsOOONOOOOOOCvOO 
CM CM CN CS CN CN CN CN CS 



00rtit-c0->-H'Or0M0J>-Or<ia\t^->-H00Of0t^O-ri^t^r0Th 
'OlO»OI:^'!:tit^OOOOCSVOasfOa\O^OOONC\ON'r-i'*ONCN 



'*c<!CNCN(>ac<icNcr5fOfOcO'*'*csir<irovo^oiocM-<*vo 



ro lO t-- l>- O fO t~^ t^ i>. t^ Jr^ !>- -^ lo 

oOt^OOOOiOtOT-iiocoO^^OOOvOMDOOOCNiOiO 



«M <N O O O 



■rH■^(^^c<^cslc^^cs^cscNcO'*fOlO■Tt^cs^c<lco^'5tlfOfOTl^co 



ONVOiOLOvOOOOiO''-iiOO'Ot^oO\Oco^CNX:^iOONfO'<* 



i-iT-4TH..-irOT-(r<icS'.-ii-i->-ii-iT-tr-iT-t 



XNaWNIVXXV 



xsax ao saaAV 



\OfOTl^ri<'^t^vOOOOOrOiOiOl>-OOOsfOrOt^OO>Ot-^OOs 



3aaM Had noix 
onnxsNi ao xsod tvxox 



CNCvJcorOcsr^i-^rt'rococNCSTH'r-icsiocr-icocsrOt-icses 



saaAV 
aaa Aanxs anon shiioh 



xaaA\. 

HaJ lOOHDS NI SHflOH 



t-~ t^ t^ O O to O O O O r<H~~t^l:^ 

lO-r-lOOOOeSCN-r-lOvOOVOlOCMOOOO'^THTHTH 



CNCNOOOOt-HtHCSO'-hO 



CSCSCOfOCSCNfOCOCSCOCSCN^— !•<— ICNrO-rHCNCSCN(^<I 



AxniaviHVA 



XNaHNIVXXV 



Ti<iOT-n>.fOiOOfOiOOCNOO-^OMDO\OiOOONfOO 



OrO'^vD'^COiOt-OOOOOOCNO^OCNOOO'd^CsfOOO 



ONOOsOOOOOiOfOOOJ>-00'^00'<-iOiOOCN<~Oto 



rovOOsvOONCNOr-'^cs-rHOOCNCNTtiroO'^iO'xhiiOrtHtO 

CN-^f-lTHr-lfOCMCNCSCOCSCSrOtO^THT-HCvICNCST-ICSICN 



aavHO 






HaHDvax 



OOONO''-iCSro^iOMDJr^OOONO'>-irs|rO'*iO\Ot^oOONO 
T-HT-icNCNCSCNCSCsiCNCNCNrsirororOfOfOfOfOfOcofr)"^ 



QQQQQQQQQWWWWPiqfiqpiHfepiHfiHOOOO 



Attainment in Classes 



45 



XSHX ^O XHSM 



HaaM H3J NOIX 
■DIIHXSNI aO XSOD TVXOX 



xaaA\ 
Had Aanxs anoH shiioh 



HaaM 
iia<i qooHDS Ni sHnoH 



AxniaviHVA 



XNaHNIVXXV 



OT Axnvn5 xNao ^aa 



6 AxiTvnb XNaD naj 






'^OOOOOOOOOOOOCOOOO 

' d d d d d d d d d d o d ' d d d 



lO 1-^ rj^ GO O 00 lO lO lO 
CSOOfOOsOMOT-l'OCSTHi-ICSHr^t^CNlOlO 



th cs csj <N CO ro ^-t CO ra CN th CO ■«-H 



io<M»oi>-r<»vocovoTt<'<-HioONO<Mr^r^oo 
^-1 Th T— I rH CO ■»-' T-H •"^ CN CO '-H 



saaM Had noix 
onHXSNi ao xsod tvxox 



O On tH vO -rH On T^ -^ CSI 00 CS vO VO •«-* O 0\ 
CS(MO\C00NON00rt^ONC0Ov>OtovOt^t-~*O 

CS CS ^-H CO CS tH tH r-l tH ■^ CO f-l t-I »-• CO •»-< 



HaaAV 
Had Aanxs anon shiioh 



CO CO *>■ O O lO 

coOOOiOOOMDiOOtOOc<lOOOOO 

coo cs O •^ T-i ^ cs t-i o ■<-< cs th o O O 



saaAv 

Had qOOHDS NI SHnOH 



COCOCO'>*-rJ<COTHCMCST-lrHlOCST-ICNtO»H 



> 



xsax ao saaAV 






XNaWNIVXXV 



TtioOOOtooOcoir-'.-i-^vOTticoOOvO'^iO 
CNCOCNCSCOCOiO^OvOO'^fOOMDCOCOlO 



toioioioioioi^^t^t-^t^ioiot^t^ioiot^ 



HaHDvax 



•.-HCSC0'Tt<»O'Olr^00ONO'«-tCMC0"<*iiO^0t^ 



AXID 



<i^<ij<1<j<<<<<j<JWpqpqfflOOO 



46 



Variation in the Achievements of Pupils 



xsax Ro 3aaM 



3aaM Had noix 
on^xsNi ao xsod tvxox 



3aaM 
Haj Aanxs awoH shhoh 



xaaAv 
Had qooHOs ni shhoh 



AxmaviHVA 



XNaWNIVXXV 



01 AxiTvnb XNaD naj 



6 Axiivn?) XNaD naa 



OOvOO"0^vO^OO^»OtOvOiOiOOiOVO»OiOtO\OiO 

cs CM ■.-I rH rH T-4 T-( th es cs cs cs r<) €s csjcMCM r^ 

r-^y-i r-i tH »-l tH ,-H tH T-H T-( tH i-l CN •rH T-H tH CS f-( fM rH 

cscNOOOOOO-^OiOOr^t^OOOOOOOOO 

T-I -.-t d d d d d d -r-I d * d ' '<6<6c>c>(6d>d>cid> 

lo lo ^o for^t^t—t^ lo lo cs es t^ t^ t- i>. 

CSCSOOfO»OOOro^'0*0'OiO«MiOCNO\0\^0^>0^ 

t— 

T-(i— ItH^-Ht-( -T-lT-iT-l^-HT— I^— I^— ItHt-(CStH tH^-H 

^— I 
lO-^t^rO lO tH O PO •^ fN vO CS fO O 

odoooooodoocNO-^cNO\0\ooodo\d 

OiocoTtt-^forOoOT-iroONOOLOOoocooocsroOT-it^ 
-^ CS fO 1-1 <r5 CS CN CS •.-H CN CN T-^ tH CN fC -^ cs cn 

1-1 tH ^-) CO i-t 1-1 1-1 <N T-( vO Tt< f<5 "^ <M <M 

0\C^iHv0t^vO00Oi-it^»OCS00iOP0iOC0Of0lr-^Oi-tiO 
00iO0\0Ni-i0\000N0\^0OsC50OO»OT-tv0000N0000t--t^ 

1-1 cs fO cs ro cs 1-t iH cs CO 1-1 th <n i-< lo cn ro «vj fO »h CO CO 

t^cs CM c^ coco t—t^ CO 

T-c^OOOO-^-^OCXJOOOOOOvOvOiOCOOOOco 

cs cs O O O O cs o 1-1 1-1 O i-< 1-1 CM CO O O 1-1 

t- ir^ so CO l>.t^CNCOOO to 00 u^ 

i-iiOTHi-*00OOv0'*00OOi>-OJ>-»O»OOOv0»OOO 

CN <M CO CO CO CO T-l T-l (N CO CN CS CS i-l r^i CM CN <N CN CN CS (N 
00^00'OOOOvO»0»OVO»Oi0^iO^O>0>0>0^»0 

(N CN 1-t 1-t 1-1 1-« 1-t cs CM cscs cs es cs cs cs CM es 

cOOt^OO^i-^CNOOOOiOiOOOOOO-^iOOOv 

'Or<li-iOI>-OONr<|i-iOsvOcoOCS«Ot^O<MCO'^CSCNO 
lO'^LO'^'^^MDLOvOOcOTt^iOOvOOeNCOiOiO'shfOiO'O 

pq <:<! pq < < pq <; pq < < < pq < 

000\OiHCSC0-<*lO^t^000\Oi-<CSC0Tt<lO^t^000\O 
i-tTHCNOqCNfNCNCSCSCSCNCMCOCOCOCOCOCOCOCOCOCO-^ 



HaaM Had noix 
onnxsNi ao xsod tvxox 



xaaAV 
Had Aanxs awoH snnoH 



xaaM 
Had qooHDS NI snnoH 



> 



xsax ao saaM 



XNaWNIVXXV 



aavHO 



HaHDvax 



AXID 



CHAPTER V 

THE MEASUREMENT OF CLASS SIZE^ 

Section 1 

The Attainment and Overlapping of Classes in 
Table VI 

If we consider for all systems the attainment of groups 
smaller than thirty-five and larger than thirty-five in each 
of the subjects, arithmetic, spelling, English composition, 
handwriting, and range of vocabulary in terms of the tenta- 
tive standards 2 suggested, no groups possess superiority by 
virtue of size. For example, (see TABLE VIII) in the fifth 
grades the large classes are superior in arithmetic, writing and 
composition, but inferior in the other traits. In the seventh 
grades the small classes are superior to the large classes in range 
of vocabulary, arithmetic and spelling ** at grade," equal in writ- 
ing and spelling measured by "higher grade" and inferior in 
composition. 

A significant measure of the influence of the size of groups 
should be found in the effect which the size of group for four 
years may exert upon attainment. To test this hypothesis the 
attainment by small and large groups for these years has been 
compared with the tentative standards suggested above. By 
this method we measure the amounts of growth which children 
taught in classes of various sizes for four years are able to make 
in terms of a standard. 

1 This chapter includes quantitative studies only. No summaries of 
present practice are attempted. 

2 See Chapter III. 

3 For additional measurement of class size using data of Table VI see 
Appendix IV, page 107. 



47 



48 



Variation in the Achievements of Pupils 






•rH 0\ ■* CS 00 O ■^-tOvT^ICVl OOOO <N (N CS CM 



On-* Oa> O cm 



\0 y-f^ ■'-* 
lO CO VO lO 



VO •<-< CS CXI 
lO fO O O 



lO O 1-1 00 
CO-* vo VO 






"<*»00^ OOOO vOtJhvO-* 



lO-* 



OOl-lT-lTtl 

■<:t< VO OOt^ 



00 0\0 CS 
rt COO lO 



OOOO OOOO OO OOOO OOOO OOOO OO OOOO 



O»0ioro 
CO 



■* vOO"* 
^ fO CN est 



■* OiOco 

t-H CO CO 



0\0 OiO 

CM 



OOOO OOOO OO OOOO OOOO OOOO OO 



to On O CM 
"* CM 



00-*l>- O 
l-H CO i-l 



loro-*"* 
CM y-i 



OOOO 

CO Ovt^ i-l 









t^O 
CMiOi-Hi-i 


00»OlO 


lOO 

CN lO 


ooiot^o 

i-H CM ■<-i ■<-( 


lOrHO 
vOt^ CMO 


to COO 
to CM rt< CO 


COO 
CO i-H 


tOrJHO 
CM CM On »H 


OOth^ 


•<-i CM Oro 


OO 


tH CM 1-1 T-l 


OOOO 


OCNCM-r-l 


OO 


OCMO-rH 
tH 1-1 tH ^ 



^ >. 



p^ 



tg-^ 



OOtHIO o o vo 0\ OOOtO -^in OOOtO 



"*C01>-vO 
CM CO to vO 

* * 



r*H CM 
rjfco 






tO'^ON'O toco torjitot^ 



0\CM On-* 
fOTt<t^ 00 



00 tH CM NO 



-^00 

t^ 1-1 

vOt>> 






cOt-ItHVO t^O'^O 



l>.O-rH\0 OOOOO t>-OOrj< oo\ ooovo 



CO ON 00 ON 
■»Ht^ Ot^ 
CM 1-H CO CO 



NO lOt^ O CM -rh 

t^ 1-1 to o o 1-H 

1-t CM CO CO CM CM 



NO to 00 On 
t-- 1-1 Oi^^ 
1-1 CM CO CO 



On CM NO 1-1 
NO On CM ''ti 
i-( 1-1 CO <>J 



t^r}< OOrH 
tH 00-* CM 
CM CMrJ< lO 



thco 
■* lO 
CM T-l 



On to NO On 
NO 1-1 CM J>. 
1-* CM CO CO 



0) 






Q> 



0) 
ct5 



>rt 



t/5 






»-i as 
+3^ > CD 

y=i^ to Qj 

^, cG ^, w 



0) 

Hit 



>3^ 



^ "*^ oi G 



tn 



w 



w 



w 



si 4J • -t-> 
40 15 W 4-3 W 



_H<ijw<uwpQaJc«a3corN(uw^cut«a)c«Ci(Uwa>wCi3a^waJOTr>i(Uw;^a^ 



Measurement of Class Size 



49 



In the fifth grades ^ the large classes are superior in English 
composition and arithmetic, nearly equal in writing and in- 
ferior in the other subjects. In the seventh grades the large 
classes are superior in writing but inferior in the other traits. 
It is evident from this that in the long run large classes exert 
some influence upon attainment. ^ The findings of this study 
yield no correlation with size of group for results taken in a 
single year. Undoubtedly the effect of size of group in a lim- 
ited time is negligible. Our measures, however, suggest the 
possible negative effect upon attainment in a period of years. 

TABLE VIII 

Per Cent of Classes in Each Group Reaching Standard Medians. 
Based on Size of Group in Which the Measures Were Taken 





Compo- 
sition 


Arith- 
metic 


Range 

of 
Vocab- 
ulary 


Writing 
Quality 


Spelling 

At 
Grade 


Spelling 
Higher 
Grade 


All Systems 

Small fifth grades 

Large fifth grades 

Small seventh grades . . 
Large seventh grades . . 


25.0 
57.14 

44.44 
55.60 


25.0 
42.9 

77.8 
22.2 


75.0 

35.7 

44.4 
22.2 


87.5 
93.0 

88.9 
88.9 


75.0 
50.0 

22.22 
11.11 


62.5 

57.2 

44.45 
44.45 


Per Cent of Classes i 
Based oi 


TABLE IX 

n Each Group Reachin 
^ Size of Class for Fouj 


G Standard Medians. 
El Years 




Compo- 
sition 


Arith- 
metic 


Range 

of 
Vocab- 
ulary 


Writing 
Quality 


Spelling 

At 
Grade 


Spelling 
Higher 
Grade 


All Systems 

Small fifth grades 

Large fifth grades 

Small seventh grades . . 
Large seventh grades. . 


20.0 
23.5 

57.1 
45.45 


20.0 

48.2 

71.4 
27.3 


100.0 
41.2 

57.1 
18.2 


100.0 
90.0 

85.7 
91.0 


100.0 
47.1 

85.7 
18.2 


80.0 

47.1 

42.8 
33.4 



5 See Table IX. 

^ Of course the attainment is influenced also by the ability of the teacher 
and no data are at hand to evaluate such influence for four years. 



50 Variation in the Achievements of Pupils 

Section 2 

The Amount of Overlapping by Grades and 
Half Grades 

overlapping of small and large classes in the 
separate systems 

In this section the comparative attainment of large and small 
classes is measured by amounts of overlapping. The per cent 
of overlapping is a significant measure because it gives us at 
once a measure of comparative status and growth and when 
computed for the systems separately gives due weight to any 
special cause which may be operative. With overlapping 
defined as it has been in Chapter III, the method has been to 
determine by counting from the arrays of the actual scores 
made by the pupils in each of the classes, the number of pupils 
who reach or exceed the median of the 7 A' grade in the subjects 
of arithmetic and composition. In spelling the method followed 
is that described in Table X. 

The accompanying table should be read as follows : In Systems 
A, B, and C, of the pupils in Grade V who reach or exceed the 
median for pupils in Grade VII, there are in arithmetic, 18.8 
per cent, in composition, 4.5 per cent, and in spelling, 19.9 per 
cent. Of the pupils in the smallest fifth grade who reach or 
exceed the median of Grade VII, there are in arithmetic, 24.0 
per cent, in composition, 3.45 per cent, and in spelling, 22.21 
per cent. These computations have been made not alone for 
each of the grades taken together, but also by classes grouped 
as to size. Uniformly the attainment by groups of small and 
large classes, and attainment of the smallest and largest classes 
of each grade has been studied in relation to the attainment of 
the seventh grade. Where the number of cases is sufficient, the 
median attainment of the seventh grade has been used in the 
systems that have annual promotion; in those that have semi- 
annual promotion the median attainment of the 7- A grades has 
been used. 

ARITHMETIC 

In Systems A, B and C considered together, the per cent of 
overlapping for the small fifth grades is 15.62 per cent; for the 
' The letter A throughout refers to the second half year of a grade. 



Measurement of Class Size 



51 



large fifth grades it is 20.6 per cent. The per cent of overlapping 
for the small seventh grades is 40.6 per cent and for the large 
seventh grades, 53.3 per cent. The per cents of overlapping 
for the smallest and largest grades are as follows: Smallest 
fifth grade, 24.0 per cent; largest fifth grade, 11.1 per cent; 

TABLE X 



► 



Systems A, B, C 

All fifth grades 

Small fifth grades 

Large fifth grades 

Small seventh grades 

Large seventh grades 

Smallest fifth grade 

Largest fifth grade 

Smallest seventh grade 

Largest seventh grade 

System D 

All fifth grades 

Small fifth grades (all) 

Small fifth grades (regular) . . 

I^arge fifth grades 

Small seventh grades 

Large seventh grades 

Special fifth grade 

Smallest fifth grade (regular) 

Largest fifth grade 

Smallest seventh grade 

Largest seventh grade 

System E 

Smallest fifth grade (5-A) . . . 
Smallest seventh grade (7-A) 
Largest seventh grade (7-A) . 
Grade 7B 

System F 

Grade 5B 

Grade 5A 

Grade 7B 

System G 

5 A grades 

Grade 7B 



Arithmetic 



18.80 
15.62 
20.60 
40.60 
53.30 
24.00 
11.10 
19.00 
62.20 



13.60 
16.67 
11.10 
8.50 
46.30 
65.50 
30.00 
14.30 
11.10 
54.20 
73.30 



25.00 
70.80 
68.96 
31.00 



2.56 

4.76 

60.00 



26.0 
26.5 



Composition 



4.50 

3.15 

5.51 

34.60 

64.90 

3.45 

11.60 

44.70 

80.50 



17.30 
25.00 
17.00 

9.70 
68.50 
71.70 
53.80 

8.00 
11.80 
92.30 
61.30 



0.00 
52.20 
87.10 
12.00 



4.87 
11.90 

82.75 



55.10 
89.70 



Spelling^ 



19.90 
20.10 
19.83 
50.10 
49.99 
22.21 
20.75 
57.73 
66.82 



34.60 
39.23 
31.52 
28.29 
44.20 
55.17 
55.13 
27.43 
31.88 
47.45 
50.50 



27.42 
45.00 
55.30 
55.30 



11.25 
7.93 

58.45 



27.45 
35.17 



8 The overlapping is measured as the per cent of members of a given fifth 
grade or group of fifth grades which reaches or exceeds the median of a 
seventh grade or group of seventh grades in ability to spell sixth grade stan- 
dard words. 



52 Variation in the Achievements of Pupils 

smallest seventh grade, 19.0 per cent; and largest seventh grade, 
62.2 per cent. The teachers are rated as equal in all of these 
grades with the exception of the largest seventh grade in which 
the teacher is rated as superior to the teacher of the smaller 
seventh grade. So far as influence of class size is concerned, it is 
negligible in these results in arithmetic. 

In System D, the largest per cent of overlapping is attained 
in the special class. The overlapping for the regular small 
classes is 11.1 per cent. The overlapping for the regular large 
fifth grades is 8.5 per cent. In the seventh grades, the per cent 
of overlapping for the small classes is 46.3 per cent, and for the 
large classes, 65.5 per cent. We should expect the special class 
of the fifth grade to attain the best result; however, considered 
as individual classes, the group of small classes is not superior. 
The results attained by the large and small fifth grades making 
the highest scores are not radically different. Yet it is true that 
the group of small classes in the fifth grades of this system is 
superior to the group of large classes, although the amounts 
by which they differ are not very great. It is significant that 
in the seventh grades, neither of the small classes reaches as 
high a per cent of overlapping as the poorer large class. For the 
smallest and largest classes, the amounts of overlapping are as 
follows: For the special class of fifteen pupils, 30.0 per cent; for 
the smallest regular fifth grade, 14.3 per cent; for the largest 
fifth grade, 11.1 per cent; for the smallest seventh grade, 54.2 
per cent; and for the largest seventh grade, 73.3 per cent. 
Although there are some differences between the performance 
of certain of the small and large classes, taking all of the classes 
together, the small classes do not show marked superiority. 
In System E,^ the amounts of overlapping are as follows: For 
the smallest fifth grade, 25.0 per cent; smallest seventh grade, 
70.8 per cent, and largest seventh grade, 68.96 per cent. We do 
not have in this system a fifth grade in the same half year which 
differs materially in size from the one quoted, so that it is im- 
possible to make a comxparison of any value between fifth grades. 
However, we have the data by which to make a comparison of 
the seventh grades. As pointed out above, for Systems A to 

^ The reader will observe that the amounts of overlapping in Systems E 
and G do not differ materially from those found by Courtis between fifth and 
seventh grades in New York City. Final Report of the Committee on School 
Inquiry, Vol. I, p. 449. 



Measurement of Class Size 53 

D, the smaller classes do not appear to possess any superiority. 
This holds even when we pick large and small classes at random 
throughout the systems, and is true for the other traits as well. 

In System G, the per cent of pupils computed on the total 
number in the fifth grades that reaches or exceeds the median 
for the seventh grade is 26.0 per cent. However, the amounts 
of overlapping for the individual grades vary somewhat more 
widely than they do in System D, but not nearly so much as 
they do in Systems A, B and C. The amount of overlapping 
for the smaller grade is 11.4 per cent. In System F, we do not 
have a sufficient number of cases for determining the amounts 
of overlapping of largest and smallest classes. However, the 
per cent of pupils of Grade V-A that reaches or exceeds the 
median of Grade VII-A is 4.76 per cent. 

Throughout the grades and systems there is variation in the 
amounts of overlapping, but in no instance is the amount of 
overlapping correlated with the size of class, nor does the small 
class seem to possess any superiority. As will be shown in a 
later section, the amounts of overlapping by the grades and half 
grades in the various subjects are fairly uniform. 

ENGLISH COMPOSITION 

The amount of overlapping in Systems A, B and C in English 
composition is an exceedingly variable quantity. For all fifth 
grades in terms of all seventh grades, it is 4.5 per cent. Computed 
as the amount of overlapping for the various groups of grades, 
we have the following: For the group of small fifth grades, 
3.15 per cent; large fifth grades, 5.51 per cent; small seventh 
grades, 34.60 per cent and large seventh grades, 64.9 per cent. 
The amounts of overlapping for the smallest and largest classes 
are as follows: Smallest fifth grade, 3.45 per cent; largest fifth 
grade, 11.6 per cent; smallest seventh grade, 44.7 per cent, and 
largest seventh grades, 80.5 per cent. If there were any superior- 
ity in the small classes we should expect to find a reversal of 
these conditions. 

In System D, the amounts of overlapping for all fifth grades 
on all seventh grades is 17.3 per cent. For the exceptional class 
of fifth grade children, it is 53.8 per cent. The amount of over- 
lapping for the various groups of fifth and seventh grades is as 
follows: Small fifth grades (regular) > 17.0 per cent; large fifth 



54 Variation in the Achievements oj Pupils 

grades, 9.7 per cent; small seventh grades, 68.5 per cent and large 
seventh grades, 71.7 per cent. Here, as noted in the other 
traits, the small classes of this S3^stem are superior in the fifth 
grade. The amounts of overlapping for the smallest and largest 
classes are as follows: Smallest fifth grade, 8 per cent; largest 
fifth grade, 11.8 per cent; smallest seventh grade, 92.3 per cent; 
and largest seventh grade, 61.3 per cent. 

In System E, the amounts of overlapping are as follows: No 
pupils in the fifth grades reach or exceed the median for the 
7-A grade. The amounts of overlapping by small and large 
classes are as follows : Smallest fifth grade, 0.00 per cent ; smallest 
seventh grade, 52.2 per cent; largest seventh grade, 87.1 per 
cent. In System F, the amounts of overlapping are: For the 
5-B grade, 4.87 per cent; 5-A grade, 11.9 per cent; for the 7-B 
grade, 82.75 per cent. In System G, the amounts of overlapping 
are: For 5-A grades 55.10 per cent; 7-B, 89.7 per cent. 

In no instance cited above, where we have cases so distributed 
that we may overlap groups of classes of different sizes, do we 
find any superiority in the group of sm.all classes or in the small- 
est classes of a grade. The possible exception is in System D, 
where we do find certain correspondences. However, there are 
other factors discussed briefly in this section and in detail in 
Chapter VI, which when taken into consideration explain in 
part at least these variations. 

SPELLING 

In Chapter III sufficient evidence has been presented to 
indicate the fact that for all of the grades in all of the systems 
taken together, we have growth in spelling ability throughout 
the grades. In this section, by the same method described in 
Table X,i° the amount of overlapping of the fifth grades upon 
seventh grades and seventh grades upon seventh grades has been 
computed by large and small classes, for each of the systems. 

For detailed relationship see Table X.^i 

10 See Chap. Ill, p. 53. 

11 The fifth grades of System F constitute a decidedly inferior group. 
This statement is based on a careful study by means of the school records 
of the school population from which these children are drawn, from a study 
of the progress records of the entire school and from detailed discussion with 
teachers and supervisors. 

Where possible studies were made of the progress of the pupils in the 
systems in which the tests were given. It was not possible to get the extended 



Measurement of Class Size 55 

Before discussing further the facts cited in the preceding 
paragraphs it should be noted that amounts of overlapping for 
handwriting measured for quantity and quality and amounts 
of overlapping for range of vocabulary have not been computed. 
As pointed out earlier in this chapter there is such close corres- 
pondence in the scores and variabilities for handwriting for the 
different classes of the various systems that any amounts of over- 
lapping which might be computed would not be symptomatic 
measures. Possible reasons for this close correspondence have 
been suggested. Amounts of overlapping for range of vocabulary 
could not be computed, because we do not now know the relative 
difficulty of the words. Our lack of knowledge of valid quanti- 
tative standards for handwriting likewise makes it impracticable 
to infer anything from the amounts of overlapping. 

The variations in the data suggest at once that there is no 
superiority in the small classes of these systems by virtue of 
the mere fact of size with the teaching ability equalized in the 
groups. 12 xhe great variability in overlapping and growth need 
not disturb us. It is somewhat disappointing not to be able 
to have amounts of overlapping or growth correspond as precisely 
as they would were our instruments of measure more refined. 
We have, however, a sufficient body of data, if used intel- 
ligently with that in the preceding chapter, to furnish a basis 
for standardizing roughly the amounts of overlapping and 

data which would be necessary for a very comprehensive study of this topic. 
So far as the facts could be studied it was evident that attainment is corre- 
lated positively and to a high degree with progress. This is what might be 
expected if children are classified in an intelligent way. However, it should 
be mentioned that the potency of such a force may not be neglected in the 
estimation of the probable effect of other factors. This has been done as 
far as possible. 

12 The facts cited above with reference to the relationship of attainment 
and class size are based upon an intensive study of tests given to forty classes 
in five subjects. Each class was given ten tests, one in spelling, three in 
range of vocabulary, one in arithmetic, one in composition and four in writ- 
ing. The same facts are corroborated by the results of the tests given in 
the classes in Systems H and I which are described in detail in later sections. 
Altogether the results of the various tests in the nine systems studied sum- 
marize the performance of about 12,000 children. For the purpose of study- 
ing promotion rate all of the classes in Systems A-F (about 400 classes) were 
studied. 

All of the facts cited in this section and in later sections for classes of 
the elementary school are abundantly supported by the facts which were 
obtained from a study of the records of seventy-five high school classes in 
three subjects. These represented a random selection from one hundred 
and sixteen classes which enroll about 3,500 high school students. 



56 Variation in the Achievements of Pupils 

growth we should expect to find between the fifth and seventh 
grades. 

Section 3 

Attainment and Class Size in Other Systems 

In this section is presented a study of attainment in oral 
arithmetic in classes of different sizes, and a study of the 
amounts of growth in classes of different sizes in the subjects 
of handwriting, language, and spelling for a period of seventeen 
weeks as indicated in the table. 

These scores represent the work of about ten thousand children 
in four hundred forty-four classes in two large city systems. City 
H is a New England city of 40,000, and City I is a city of 25,000 
in the Middle States. The measurements were made by a 
competent man at the time he was superintendent in each of 
the cities. 13 The tests were given under controlled conditions, 
uniformly scored by an experienced teacher and, although there 
may be some differences between the status assigned to a pupil 
by this method and the status which would be assigned by 
the use of scales of measure similar to those used in Chapters 
II and III, in evaluating the achievements of pupils, neverthe- 
less, it is sufficient to say that the relative findings in the classes 
of different sizes would not be displaced very much. For de- 
tailed discussion of the tests and the method of giving them, 
see the Appendix, Section II. 

In City H, eighty-three classes were measured in handwriting 
on December 4 and again on April 12 of the same school year. 
The time which elapsed between these dates represents seven- 
teen weeks of school. The papers were scored by an experi- 
enced statistical clerk, who used the Thorndike scale. It is 
significant that the number of small classes which show no 
growth is nearly three times that of the large classes; it is even 
more significant because there are slightly fewer small than 
large classes. The lowest per cents of growth are made in the 
small classes. A far more reliable measure and far more sig- 
nificant is the per cent of classes of each size that makes a gain 

13 The claim is sometimes advanced that testing directed by a competent 
superintendent yields results of a far higher degree of validity than those 
obtained in other ways. While this is probably not a pertinent criticism, the 
opportunity to present these results for growth in classes of different sizes 
is utilized. 



Measurement of Class Size 



57 



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58 



Variation in the Achievements of Pupils 



of 15 per cent or more on the December measure. From the 
table it is seen at once that the large classes make a decidedly 
better showing. 

In language, forty-two classes were measured. As in the 
case of writing, the largest gain in points is made in the larger 
classes; the smallest gains are also made in these classes. It 
is evident that in this system no size of class possesses superi- 
ority. The gain of the median class is a reliable measure, 
free from ambiguity. It tells us the amount of gain in the 
middle of the group. If a group shows marked superiority 



Grade& 3—S 



Ml Grades 



Under 30 
Over 30 



Fig. 6. Handwriting. System H 

Per cents of classes in each grade group that show a growth of 15 per cent 

or over 



obviously its median will have a higher record. There seems 
to be no superiority in the groups of small classes when the 
classes are separated by grade-groups. If the results are tabu- 
lated to show the per cents of classes of different sizes that 
show a growth of five points or more, they are consistently in 
favor of the smaller classes. 

The total number of classes tested in spelling was twenty-five. 
These classes were in grades one to three only. In June, we 
have for small classes no class making a perfect score. In these 
same classes for those making over 50 per cent on the test, we 



Measurements of Class Size 59 

have the following records: 13 per cent, 10 per cent, 28 per 
cent, 36 per cent, 30 per cent, 59 per cent, 83 per cent, 10 per 
cent, 77 per cent, 10 per cent, and 73 per cent. In the group 
of classes of thirty and over, we have the following records 
for the per cent in each case that makes 100 per cent on the 
spelling test: 3 per cent, 4 per cent, 70 per cent, 22 per cent, 
14 per cent, and 15 per cent. Of this same group, the following 
percentages make over 50 per cent on the spelling test: 67 per 
cent, 10 per cent, 6 per cent, 65 per cent, 18 per cent, 72 per 
cent, 20 per cent, 34 per cent, 48 per cent, and 33 per cent. 
The per cent of small classes which makes 100 per cent in the 
spelling test is per cent. The per cent of pupils in the median 
class of the group whose members achieve 50 per cent or over 
is 39. In classes over thirty, the per cent of pupils in the 
median class making 100 per cent in the spelling test is 15 per 
cent; the range is 3 per cent to 70 per cent for the entire group. 
Of this group 57 per cent of the classes fail to have any perfect 
scores. The average per cent of pupils reaching 50 per cent or 
over and not making perfect scores in classes of over thirty is 
35.73. This result tallies closely with all the other results quoted 
above. In other words, the small classes do not seem to have 
any marked advantage over the larger classes. Indeed, larger 
classes are slightly superior to the small classes in a number 
of instances. 

For City I, the classes have been separated into four groups: 
Fewer than thirty-five, thirty-six to forty-five, forty-six to fifty, 
and over fifty. In language the largest percentage of classes 
showing losses are for the classes under thirty-five and over fifty. 
The largest loss made in any class is in the group thirty-six to 
forty-five, and the largest gain made in any class is in the group 
under thirty-five. The highest per cent of classes making gains 
is in the group forty-six to fifty, in which all of the classes show 
gains. In order, the other groups are as follows: thirty-six to 
forty-five, 83 per cent; fewer than thirty-five, 76 per cent; 
over fifty, 66.7 per cent. The average gain per class is largest 
in the group forty-six to fifty, next in the group over fifty. 
The smallest average gain per class is in the group of smallest 
classes. The per cent of classes which show a loss is as follows: 
In the group forty-six to fifty, per cent; in the group thirty- 
six to forty-five, 18 per cent; under thirty-five, 24 per cent; 



60 



Variation in the Achievements of Pupils 



TABLE XII 

LANGUAGE, SPELLING AND ORAL ARITHMETIC IN SYSTEM I. 

6,600 Pupils in 165 Classes. 294 Classes Reported. 
129 Classes Measured in More than One Subject 



Fewer 

than 

35 



36-45 



46-50 



Over 
50 



Language (Written Reproduction). 

Total number of cases, Grades 3-5 

Number of classes with gains 

Largest gain in points 

Smallest gain in points 

Gain of median class 

Score of class at 25 percentile 

Score of class at 75 percentile 

Per cent, of classes gaining 10 points 

Number of classes with losses 

Largest loss in points 

Smallest loss in points 

Loss of median class 

Spelling. 

Total number of classes in which 100% is scored. . . 
Highest per cent, in any class making 100% . . . . 
Lowest per cent, in any class making 100% .... 
Number of classes in which 100% is not scored. . 

Grades 1 and 2, per cent, of classes with 100% 

Grades 3-5, per cent, of classes with 100% 

Grades 6-8, per cent, of classes with 100% 

Total number of classes in which 80% is scored. . . 
Highest per cent, of pupils in any class making 

score 

Lowest per cent, of pupils in any class making 
score 

Oral Arithmetic, 

Total number of classes, Grades 3-8 

Highest per cent, scored in any class 

Lowest per cent, scored in any class 

Number of classes. Grades 3-5 

Score of median class 

Number of classes. Grades 6-8 

Score of median class 

Grades 3-5 

Score of class at 25 percentile 

Score of class at 75 percentile 

Grades 6-8 

Score of class at 25 percentile 

Score of class at 75 percentile 

Grades 3-8 

Score of class at 25 percentile 

Score of class at 75 percentile 



29 
22 
36.0 

1.0 

8.3 
6.00 
12.4 
28 

7 

9.4 

.7 

6.00 



43 
73.3 
3.0 
11 

37.1 
18.0 
20.0 
51 

80 

10 



37 

76.2 
9.0 
26 

45.0 
11 
43.2 



33.3 

55.5 



40.0 
55.0 



40.0 

53.8 



17 
14 
35.4 

2.2 

11.8 

7.60 

16.30 

50 

3 
22.1 

1.3 
15.2 



31 
65.7 

2.2 

6 
37.5 
19.2 



11 
11 
33.1 

3.6 
15.6 

4.5 
29.0 
45 









3 
2 

16.0 
9.8 
9.8 
9.8 

16.1 

33 
1 

4.0 
4.0 



15 
61.7 

2.2 

3 
53.4 
18.0 



4.00 



5 
70.5 
2.9 




36 

84.4 
2.8 



66 

69.0 
5.0 

27 

47.3 
39 
35.5 



37.8 
64.3 



26.7 
49.0 



30.0 
50.0 



19 

60.4 

10.6 



26 

63.6 

12.0 

19 

50.0 

7 
31.3 



39.4 
60.5 



23.7 
50.0 



30.7 
59.4 



21.0 
"5" 
61.7 
20.6 



11 
73.07 
29.1 

8 
36.8 

3 
36.1 



30.0 

48.5 



32.3 
50.0 



32.3 

48.5 



Measurement of Class Size 61 

over fifty, 33 per cent. There are too few cases of classes show- 
ing losses to draw any conclusions from the figures. A very 
significant measure, however, is the per cent of classes in each 
group which shows a gain of ten points or over. These per 
cents are shown in the diagram, and are indicated in the table. 
These measures, which represent growth measures for a period 
of seventeen weeks, show conclusively that there is no superi- 
ority in the small classes in this city for this subject in the 
classes measured. 

In spelling, the classes under thirty-five possess some superi- 
ority to the other groups of classes, if we regard the per cent 
of pupils making 100 per cent as a valid measure. With this 
measure, these classes are not very much superior to those 
over fifty, although the small number of cases in this group 
(over fifty) makes the measure less reliable. Using as a meas- 
ure the per cents of classes by groups, none of whose pupils 
make 100 per cent, the group of classes under thirty-five shows 
inferiority, for 25 per cent of this group includes no pupils 
that can make 100 per cent. The results for the other classes 
are: Thirty-six to forty-five, 20 per cent; fort\7-six to fifty, 20 
per cent; over fifty, per cent. The few cases in the group 
over fifty make the measure for this group less reliable than 
the others. Measured by the per cent of classes whose members 
make 100 per cent, there is very little difference among the 
groups with the exception of grades one and two, where the 
highest per cent is in the group forty-six to fifty. For the other 
measures in the table, there are no essential differences among 
the groups. 

To check these results, the per cent of pupils who reach or 
exceed 80 per cent in these various groups of classes, was com- 
puted. For the group of classes under thirty-five, there are 
fifty-one classes. Two of these classes or 4 per cent have no 
members that attain a grade of 80 per cent. The range in grades 
is from per cent to 80 per cent, or disregarding the zero cases 
from 10 per cent to 80 per cent. For those classes that do 
attain 80 per cent or more, the average percentage of children 
attaining this grade is 38.2 per cent. The median is 40 per cent. 

In the group of classes having a membership of thirty-six to 
forty-five, there are thirty-six. All of this group attain 80 per 
cent. The average per cent in these classes that attain 80 per 



62 



Variation in the Achievements of Pupils 



cent to 100 per cent is 37 per cent with a median of 40 per cent. 
The range in attainment is from 2.8 per cent to 84.4 per cent. 
In the group of classes forty-six to fifty, there are nineteen. All 
of these classes attain 80 per cent. Of this group, the average 
per cent in the classes that attain 80 per cent is 38.7 per cent 
with a per cent of forty for the median class. The range in 
percentage is from 10.6 per cent to 60.4 per cent. In the group 
of classes over fifty in membership all of the classes attain 
80 per cent. The average per cent of pupils that attain this 
record is 45.9 with a per cent of 53.1 for the median class. The 
range for this group is 20.6 per cent to 61.7 per cent. 

In oral arithmetic, the highest score made in any class is 
made in one of the smallest classes; in this same group of classes, 
also the lowest score, except one, is made. The next highest 
score is made in the group of classes over fifty, and its lowest 
score is over three times as high as the lowest score in the 
classes under thirty-five, six times that of the classes in the 
group thirty-six to forty-five, and two and one-half times that 

60 



SO 



^ 



so 



20 



/O 



-3S 3A-'fS' ^"SO SO-t 

Fig. 7. Reproduction. System I. 
Per cents of classes of different sizes that gain 10 points or more 



Measurement of Class Size 63 

of the lowest class in the group forty-six to fifty. As measured 
by this score when the group is not separated by grades, the 
best classes are in the groups under thirty-five and over fifty, 
with no essential difference between these groups or between the 
groups thirty-six to forty-five and forty-six to fifty. The scores 
of the median class in each group present no essential differ- 
ences. The range in ability among the classes in each group 
is indicated by the percentiles in Table XII. 

In the studies of attainment, variability, and measurements 
of growth, in the classes of Cities H and I, no essential differ- 
ences are evident among the classes of different sizes. The 
results are entirely comparable, because the testing was done 
under the direction of the same superintendent. It is signifi- 
cant that with entirely different cities, with different popula- 
tion groups, with different types of school organization, results 
taken for the sole purpose of studying the improvement made by 
children show no correlation between class size and attainment. 

Section 4 
Class Size Measured by Promotion Rate and Expenditure 

That this question might be studied from every important 
angle, complete data upon salaries and promotion rates were 
collected in all of the systems. For all of the systems the 
resemblance between the class size and the rate of promotion 
has been measured by the Pearson coefficient. ^^ This has been 
selected because it gives a more precise index of relationship 
than is shown by roughly grouping rates of promotion by class 
sizes and averaging them. This latter method has been used 
for a few of the cities, and in addition, the resemblance between 
class size and promotion rate has been measured for all the 
classes of sizes sixteen to twenty, twenty-one to twenty-five, 
twenty-six to thirty, thirty-one to thirty-five, thirty-six to 
forty, forty-one to forty-five, forty-six to fifty, and over fifty. 
In no instance is the relationship different from that shown in 
the table. So far as these cities are concerned there is practi- 
cally no relationship between class size and promotion rate. 

If one were to select a single fiscal measure as symptomatic 

1* The student not familiar with statistical technique will find explanations 
of the method used in Thorndike's Mental and Social Measurements, Chap- 
ters X and XI (1913 edition). 



64 



Variation in the Achievements oj Pupils 



of a school system's condition, he would be justified in using 
teachers' salaries for the reason that teachers' salaries, roughly- 
speaking, constitute about three-fourths of the budget in Amer- 
ican cities. Accordingly the relationship between teachers' 
salaries in these systems and class size has been calculated by 
the Pearson coefficient. As in the case of promotion rates, the 
coefficients indicate a lack of relationship. Although no claim 
is made that this absence of relationship applies to anything 
except teachers' salaries and class size, it probably is sympto- 
matic of the relationship of the entire budget to the class size. 

TABLE XIII 



Class Size Correlated With 



Promotion 
Rate 



Teachers'! 
Salaries 



Systems'! B 
IQ 

System D 

System E 
System F, 



— .04 
+ .12 

+ .116* 

— .07 



— .29 

— .08 
-.11* 

+ .07 

—.15 



* Figures for February, 1914. 

1 Data for System G incomplete. Such computation as could be made 
indicates the same general lack of relationship. 



Section 5 

The question of class size has been studied in some detail by 
a number of investigators. The most important contributions 
have been made by Rice, Bachman, Cornman and Boyer. 

In two extensive investigations Dr. Rice studied among 
other things the attainment reached by pupils in the elemen- 
tary school in classes of different sizes. He tested six thousand 
children in arithmetic. These pupils represented a sampling 
of the fourth, fifth, sixth, seventh and eighth grades in eighteen 
bmldings of seven cities. In discussing this experiment Dr. 
Rice says: 

" That the amount of resistance offered by non-pedagogical 
influences is to-day unknown does not by any means indicate 
that it must forever remain unknown. On the contrary, the 
problem of modifying conditions is not at all difficult to solve 



Measurement of Class Size 65 

if we will but look it squarely in the face, divide it into its com- 
ponent parts, and study each factor independently. Analysis 
of the problem will show that the essential elements of which 
it is composed do not exceed three in number: (1) The home 
environment of the pupils; (2) the size of the classes; and (3) 
the average age of the children." " 

In his preliminary report of this investigation, Dr. Rice says: 
*' The size of classes must also be ruled out, the results being 
just as liable to be favorable in large as they are in small classes."^' 

In his final report upon arithmetic and class size he concludes : 

** Equally surprising, if indeed not more incredible, may appear 
the statement that no allowance whatever is to be made for the 
size of the class in judging the results of my test. I shall not 
enter into the details in regard to this point, but will dismiss it 
with the remark that the number of pupils per class was larger 
in the highest six schools than it was in the schools of City VI, 
and that the classes were exceptionally small in the school that 
stands at the lower end." " 

Dr. Rice also studied ^^ the attainment in language in classes 
of different sizes of eight thousand three hundred children in 
twenty-two buildings in nine cities. The tests were given to 
pupils in the fourth, fifth, sixth, seventh and eighth grades. In 
his report upon class size and attainment he concludes : 

" It has always been supposed that the size of the class must 
necessarily exert a powerful influence on the results. But 
investigation showed that there was no relationship between the 
size of the class and the results, and that some of the best work 
had been done in the largest classes, and some of the poorest 
in the smallest classes." i' 

Dr. Rice's measurements in classes of different sizes of four- 
teen thousand three hundred children in sixteen cities were 
conducted with great care. No one has ever successfully dis- 
proved his conclusions, but, on the other hand, they are ac- 
cepted by every competent student of education as among the 
best examples of scientific work in education and are regarded 
as highly trustworthy. 

15 The Forum, Vol. XXXIV, No. 2, p. 286. 

^^Ibid., No. 1, p. 124. 

^^Ibid., No. 2, p. 286. 

^^Ibid., Vol., XXXV, No. 2, p. 269. 

" The Forum, Vol. XXXV, No. 3, p. 445. 



66 Variation in the Achievements of Pupils 

In an exceedingly careful investigation made in 1909, Dr. 
Commando showed that there is no relation between the promo- 
tion rate and class size. He utilized the records for three 
hundred twenty classes which include all of the classes of District 
No. 6 of Philadelphia for the term ending in January, 1909. 
Since the number of cases is sufficient upon which to base con- 
clusions, and since the study was confined to a single district 
in which the policy in regard to promotion is perforce more 
uniform than it can be in all of the districts of any large city or 
in any series of cities under different supervisory management, 
his results possess a high degree of validity. In the following 
pages there are quoted the essential tables and arguments 
presented in this study. 

** It has been taken for granted, therefore, that large classes 
are to be counted among the important causes of retardation 
and, conversely, that much better results are secured with classes 
small in size. Such assumptions as these are quite natural. 
Indeed, it seems almost self-evident that a teacher would do better 
work with a class of 30 than with one of 40, and that the adverse 
conditions to be met with in a class of 50 or more pupils must 
surely be reflected in a marked deterioration in results, if not in 
complete failure. This view of the relation of the size of the class 
to the efficiency of the teaching is held so strongly, that the 
demand for smaller classes is practically universal, and many 
school superintendents are concentrating their attention upon 
the problem of reducing the size of their classes from, say, 40 
to 50 pupils per teacher to classes ranging from 30 to 40. But 
the number of pupils per teacher can be reduced only by em- 
ploying more teachers, so that the question becomes an im- 
portant one from the economic point of view. For this reason, 
and also for the pedagogical interest inherent in the problem, 
the influence of the size of class upon the progress of the pupils 
is worthy of careful investigation. 

"A method by which such investigation may be made is to 
examine the relation of the size of the class to promotion per- 
centages, the latter constituting a convenient measure of rate of 
progress. This method was employed with the promotion 
records for January, 1909, of the schools of District No. 6, 
Philadelphia. The classes were arranged according to size in 

20 The Psychological Clinic, Vol. Ill, No. 7, pp. 206-212. 



Measurements of Class Size 



67 



three groups: 'under 40,' '40 to 49,' and * 50 or over,* and 
the promotion percentages determined for each group. The 
results are given in Table I, for each grade separately, for gram- 
mar grades (5th to 8th) and for primary grades (1st to 4th) 
taken together, and for the totals of all the groups. The last 
line of this table shows that there were 83 of the ' under 40 ' 
classes with an average membership of 36 and that 83.2 per cent 
of the pupils in these classes were promoted ; that the * 40 to 49 ' 
group consisted of 176 classes with an average membership of 
45 and a promotion record of 84.5 per cent; and that 61 classes 



TABLE I 
Promotion Percentages, January, 1909 

Classes Grouped by Size 





Under 40 


40 to 49 


50 


or Over 


Grade 


No. 


Av. 




No. 


Av. 




No. 


Av. 






of 


No. 


Pro- 


of 


No. 


Pro- 


of 


No. 


Pro- 




Classes 


Pupils 


moted 


Classes 


PupHs 


moted 


Classes 


Pupils 


moted 


8 


9 


34 


89.2 


7i 


44 


90.0 











7 


10 


36 


84.9 


8i 


45 


91.9 


4 


51 


92.1 


6 


9 


30 


86.4 


19 


45 


84.1 


4 


52 


89.4 


5 


11 


36 


83.4 


25 


45 


87.3 


5 


54 


87.0 


4 


8 


38 


81.2 


33^ 


45 


84.2 


4 


52 


84.6 


3 


11 


36 


87.9 


28 


45 


84.6 


12 


53 


80.8 


2 


13 


36 


79.4 


32^ 


44 


85.1 


9 


53 


74.2 


1 


12 


36 


76.0 


22 


46 


76.4 


23 


54 


76.7 


Gram 


39 


36 


85.8 


60 


45 


87.3 


13 


53 


89.3 


Primary. . 


44 


36 


80.9 


116 


45 


83.0 


48 


53 


77.9 


Total.... 


83 


36 


83.2 


176 


45 


84.5 


61 


53 


80.3 



with an average membership of 53 had a promotion record of 
80.3 per cent. The highest promotion record, therefore, was 
made by the classes of medium size and the record of the group 
of * 50 or over ' was but 2.9 per cent below that of the ' under 
40 ' group. Similar comparisons may be made for each grade 
separately or for the grammar grades or primary grades taken 
together. Some of the facts of Table I are given in chart I 
in order to facilitate such comparisons. Examination of this 
chart discloses that in the 1st, 4th, 6th and 7th grades and in 
the grammar grades as a whole the best promotion records were 
made by the largest (50 or more) classes; that in the 2d, 5th, and 



68 



Variation in the Achievements of Pupils 



8th grades, in the primary grades as a whole and in all the grades 
taken together, the medium-sized classes had the best pro- 
motion records; and that in only one grade, the 3d, did the 
smallest classes have the best record. The chart also shows that 
for the 1st, 4th, 7th, and 8th grades and for the grammar grades 
taken together the promotion percentages for small, medium, 
and large size classes increase in the order given, or, as it may 
otherwise be expressed, the larger the class the better the record. 
'* In general, it may be said (a) that careful scrutiny of the 
facts of Table I or their graphic representation, Chart I, fails 
to reveal any advantage in small classes over classes of medium 
size as regards promotion percentages; {h) that the classes of 

TABLE II 
Rating of Pupils, February, 1909 
per cent " satisfactory " in school work 
Classes Grouped by Size 



Grade 


Under 40 


40 to 49 


50 or Over 


8 


61 


59 


66 


7 


67 


60 


72 


6 


55 


61 


64 


5 


57 


68 


61 


4 


70 


69 


68 


3 


72 


69 


72 


2 


60 


69 


75 


1 


73 


76 


56 


Grammar. . 


59 


61 


65 


Primary.. . 


71 


69 


70 


Total... 


64 


69 


67 



medium size make, on the whole, the best showing ; (c) that the 
large classes do not, on the whole, fall much below the other 
groups ; (d) that in the grammar grades, the larger the class the 
better the promotion record. 

" To secure additional data upon the relation of size of class 
to rate of progress, the monthly report cards (for February, 
1909) upon which the teacher records her rating of the pupil's 
conduct or deportment and his progress in school-work were 
utilized. The percentage of the pupils of a class rated as making 
satisfactory progress was determined and the classes were then 
arranged in groups according to size. The results are given in 
Table II and displayed graphically in Chart II. 



Measurements of Class Size 



69 



" Examination of this chart shows that in the 2d, 6th and 8th 
grades, and in the grammar grades taken together, the largest 
classes make the best showing; that in the 1st and 5th grades and 
in the total for all grades the medium sized classes have the best 
record; and that in the 4th and 7th grades and in the primary- 
grades taken together the smallest classes have the highest 
ratings. On the whole, the pupils of the medium size classes 
have the best ratings and those of the smallest classes the poorest, 
while again, in the case of the grammar grades, the larger the 
class the better the rating. 

TABLE III 

Rating of Pupils, February, 1909 

per cent " satisfactory " in conduct 

Classes Grouped by Size 



Grade 


Under 40 


40 to 49 


50 or Over 


8 


80 


85 


96 


7 


76 


85 


80 


6 


66 


84 


83 


5 


78 


80 


82 


4 


89 


78 


89 


3 


88 


78 


90 


2 


89 


80 


86 


1 


90 


85 


87 


Grammar. . 


77 


85 


87 


Primary.. . 


89 


79 


90 


Total... 


84 


79 


90 



** Discussion of these results in a meeting of school principals 
gave rise to the suggestion that the comparatively poor records 
of the smaller classes might be compensated for by a * moral 
gain ' which could not readily be measured. In order to attempt 
some measurement of the * moral gain,' the monthly report 
ratings for * conduct ' were also tabulated. The results are 
given in Table III and in Chart III. The chart shows clearly 
that the percentage of pupils rated as satisfactory in conduct is 
greatest in the largest classes, whether we group the classes by 
primary grades, by grammar grades or consider the entire 
number of classes without regard to grade ; and again in the gram- 
mar grades, the larger the class the better the result. The 
pupils of the classes of meditmi size are not rated so high in con- 
duct as those of the small and of the large classes. 



70 Variation in the Achievements of Pupils 

"A review of Charts I, II and III seems to indicate (a) that 
size of class is not a very important factor in the determination 
of rate of progress or retardation of the pupils of the class, (b) 
that medium size classes (40 to 49 pupils) make somewhat the 
best showing, (c) that large classes (50 or more pupils) make a 
poorer showing in primary than in grammar grades, and — as a 
corollary of (c) — (d) that it is more important to have small 
classes in the primary than in the grammar grades. The usual 
practice, however, is to overcrowd primary classes while grammar 
classes are relatively small." 

More recently the promotion rate for classes of different 
sizes in the city of Philadelphia has been studied by Boyer." 
In the succeeding paragraphs there are quoted tables and sam- 
ple arguments from this study. 

** In order to discover the relation existing between the size 
of classes and school progress, an investigation was made of 
the promotion records for June, 1913, of the public schools of 
Philadelphia. In each of the city's ten districts, the classes 
were divided according to size into six groups as follows: under 
30, 30 to 34, 35 to 39, 40 to 44, 45 to 49, 50 and over. The 
percentage of promotion was then determined for each group. 
Individual classes showed the widest possible variations in 
promotion percentages, there being one class in which no pro- 
motions were made, and several in which 100 per cent were 
advanced. In general, however, the variation was limited to 
a range of twenty points from 75 to 95 per cent with the highest 
rates occurring most frequently in the upper grammar grades. 

" That school progress, as indicated by promotion percentages, 
does not vary greatly save in exceptional instances, is indicated 
by table II, where percentages are given for each grade in each 
group. Nevertheless, that minority of pupils fortunate enough 
to find themselves in small classes would seem to be the favored 
few. 

" The complexity of the situation, the many diverse factors 
which enter into promotion, do not warrant us in expecting to 
find a regular and gradual decrease in promotion rates as classes 
increase in size. But table II shows some glaring irregulari- 
ties, e. g. the lowest percentages in four grades, (8th, 6th, 4th, 
1st), are found in the group next larger than the one showing 

21 Psychological Clinic, May 15, 1914, Vol. Ill, No. 3, pp. 82-90. 



Measurements of Class Size 



71 



the highest percentage. Again, in the fifth grade an exception- 
ally low percentage is shown in the smallest size group. This 
represents only one class, however, and is an illustration of the 
operation of other forces than class size. It is probable that 
in this small class were concentrated the 'slow' fifth grade pupils 
of the school concerned in order that special attention might 
be afforded. That such irregularities are exceptional is indi- 
cated by the fact that on massing together the grammar classes, 
the highest percentage, 88.2, falls in Group II, even though 
Groups I, II, and III, have shown three lowest percentages. 
The same is true of primary classes which show two lowest 

TABLE II 
Promotion Percentages in Each Grade-group — District No. 7 





Grades 








Groups 


8 


7 


6 


5 


4 


3 


2 


1 


Total 


I. ( -30) 
II. (30- 4) 

III. (35- 9) 

IV. (40- 4) 
V. (45- 9) 

VI. (50+ ) 


88.3 
90.3 
84.5 
89.8 
89.0 


8615 
85.7 
83.4 
66.7 


96.4 
76.4 
78.2 
81.7 
81.9 
81.7 


62.5 
87.9 
82.5 
83.2 
80.4 
80.5 


87.0 
70.7 
84.4 
81.2 
82.8 
79.7 


94! i 

85.0 
82.5 
81.4 
77.3 


si.'s 

82.9 
82.5 
77.8 
82.0 


90.8 
70.9 
73.9 
81.9 
74.9 
73.7 


85.3 
88.2 
83.1 
83.9 
81.9 
80.1 


89.4 
73.7 
81.1 
82.0 
79.1 
78.8 


87.4 
79.5 
81.9 
82.8 
79.9 
79.1 



percentages in Group II, while the highest percentage for total 
primary is found in Group I (89.4). In the total of all grades 
the highest percentage, 87.4, is found in the smallest group, 
and the other percentages vary less, as might be expected. 

" The irregularities of table II, together with the fact that 
a somewhat similar investigation pursued by Dr. O. P. Corn- 
man, in District No. 6, in January, 1909, showed very different 
results, led to the extension of this study to include the other 
nine districts of the city. Classes were distributed into six size 
groups, promotion percentages computed, and tables similar to 
table II constructed. In none of these nine districts were the 
highest percentages concentrated so overwhelmingly in the 
smallest size groups. 

" In District No. 6, where the highest rates are evenly divided, 
the four highest percentages found in the larger classes (Groups 



72 



Variation in the Achievements of Pupils 



IV, V, and VI) are all in grammar grades. There are no gram- 
mar classes in Group I. The highest percentages are only very 
slightly in advance of the percentages shown in the smallest 
groups except in the sixth grade, where a specially low per- 
centage is shown in Group II . In the four primary grades the 
highest rates are found in the three smallest groups. (Table IV.) 
** District No. 9 is the only one having the greater number 
of highest percentages in groups of classes over forty. Exami- 
nation of table V will show that of the five highest percentages 
in larger groups, four are found in Group IV (40-4) and only 
one in the very largest group (50 and over). 



TABLE IV 
Per Cent Promoted by Grade-groups — District No. 6 





Grades 


Groups 




















8 


7 


6 


5 


4 


3 


2 


1 


1. -30 










83.6 


89.0 


62.0 


89.2 


11.30- 4 


91.8 


90.9 


64.5 




75.4 


73.8 


90.8 


87.1 


III. 35- 9 


84.0 


88,4 


86.2 


86.6 


88.7 


80.0 


83.8 


67.0 


IV. 40- 4 


88.3 


91.6 


79.9 


85.3 


85.1 


76.8 


85.5 


65.3 


V. 45- 9 


89.7 


82.6 


86.3 


83.8 


87.2 


85.9 


85.7 


77.1 


VI.50+ 


93.3 


79.8 


85.5 


86.2 


84.4 


75.0 


80.7 


68.7 



TABLE V 
Per Cent Promoted by Grade-groups — District No. 9 





Grades 


Groups 


8 


7 


6 


5 


4 


3 


2 


1 


pL -30 

IL 30 -4 

UII.35 -9 

■IV. 40 -4 

f^ V. 45 -9 

i:VI.504- 


87.0 
86.2 
78.4 
92.4 
84.4 


93.1 
91.5 
82.2 
83.5 
87.1 
90.1 


100 ! 6 
86.1 
82.3 
81.2 
87.0 


si.i 

81.6 

85.5 
83.3 
77.9 


75.9 
81.3 

85.2 
84.8 
77.2 
87.4 


89.3 
82.4 
86.7 
81.9 
81.8 
78.2 


76!9 

83.8 
87.0 
84.5 
81.6 


80.0 

72.7 
71.4 
83.1 
76.9 

77.4 



Measurements of Class Size 73 

" Further examination of table VII will show that only in 
the seventh and fifth grades is there a gradual shrinkage of 
percentages as the classes grow larger in size, but this is not 
surprising in view of the unequal distribution of classes among 
the various size groups. Moreover, the lowest rates in the 
sixth, fourth, and second grades are located in groups smaller 
than those indicating highest percentages. But these appar- 
ently unwarranted stragglers are more than counterbalanced 
by the fact that in the remaining five grades, (eighth, seventh, 
fifth, third, and first) the lowest rates are shown in the largest 
size-group, i.e. fifty and over. 

" On combining totals for the four grammar grades, a regular 
descent in promotion rate is shown, i.e. from 89.8 per cent in 
Group I to 82.5 per cent in Group VI (see column 9, table VII). 
Could we stop here, a fairly clear case for smaller classes might 
be established; but total primary rates seem to indicate that 
medium sized classes have the advantage. Groups III and IV 
show an average of 85 per cent while both smaller and larger 
groups hover around the same rate, 80 per cent. In the per- 
centages of the grand total of elementary pupils, these advan- 
tages neutralize each other and approximately the same pro- 
gress is indicated for all classes having less than forty-five 
belonging. In each of these four groups the rate is very close 
to 85 per cent and the falling off in rates shown by larger classes 
is correspondingly more noticeable. These lower rates (82.7 per 
cent in Group V and 80.1 per cent in Group VI) are seen to be 
of no mean significance when it is recalled (table VI) that 
they are the promotion percentages of 48.9 per cent of the 
total number of classes in the city, and that these classes con- 
tain 55 per cent of the total number of elementary pupils." 

The results of Boyer agree only in part with those of Corn- 
man, but do not, on the other hand, disprove the fact that no 
relationship was present in 1909 when Cornman made his study. 
Boyer does not give us a complete distribution of percentages 
of promotion by class sizes. If one carefully examines his 
tables he will note that frequently the largest classes have 
per cents of promotion that differ but little from the per cents 
in the smaller classes; however, it is true that in some instances 
the highest single per cents do fall in the group of smallest 
classes. Boyer further attempts to compute the expectancy of 



74 Variation in the Achievements of Pupils 

repetition in the grades without considering individual histories. 
Again the use of records from several districts introduces an 
amount of error which he does not attempt to correct and he 
does not use so precise a measure of relationship as a coefficient 
of relationship. He frankly admits the many irregularities 
which are evident in his study. So far as his data are con- 
cerned there is apparently no significant relationship between 
class size and promotion rate. 

Bachman22 in his study of class size and promotion rate in the 
schools of New York City points out that although there are 
slight differences in the promotion rate in some groups of small 
and large classes these differences are not sufficient in amount to 
warrant changes in the policy of assignment 23 of class size. The 
facts and arguments are summarized in the following quotation 
from the report i^* 

" When the several grades are considered as a whole it will 
be observed that the highest per cent of promotion was in classes 
under thirty-five, the rate being 89.36 per cent. The rate of 
promotion in classes of thirty-five to forty was, however, only 
.22 of 1 per cent less, and, in classes of forty-one to fifty, only 
.41 of 1 per cent less than in classes under thirty-five. Hence, 
for practical purposes, the rate of promotion was the same in 
all classes having fifty and under. But the rate of promotion 
in classes of fifty-one to fifty-five was lower than in classes under 
thirty-five by 1.68 per cent, in classes of fifty-six to sixty by 5.91 
per cent, and in classes over sixty by 18.17 per cent. The major 
part of the difference in the rate of promotion, at least in classes 
of fifty-six to sixty, and in classes over sixty, in comparison 
with the rate of promotion in classes under thirty-five was, how- 
ever, due to the fact that pupils in the classes of these two sizes 
are principally in the lower grades, where the rate of promotion 
is relatively low. No such differences, it will be observed, appear, 
if comparison is made, grade by grade, between the rate of pro- 
motion in the classes of the several sizes. 

" The differences, such as they are, in the rate of promotion 



22 Final Report of the Committee on School Inquiry, 1911-1913, Vol. I, 
pp. 606-609. 

23 The reader is warned that this discussion refers to promotion rate only. 
No measurement of the ability of the children in these grades was attempted 
by the Committee on School Inquiry. 

2* Report of Committee on School Inquiry, op. cit. 



Measurements of Class Size 75 

within each grade, in these different-sized classes, become 
clearer, if all classes of fifty and under are combined and all 
classes of over fifty, and comparison is made between the rate 
of promotion in classes of these two sizes only. Table XVII 
gives by grades the per cent of promotion in classes of fifty and 
under, in classes of over fifty, and the per cent of promotion in 
classes of fifty and under, above or below the per cent of pro- 
motion in classes over fifty; also the increase in number of 
pupils that would have been promoted in classes of over fifty at 
the rate of promotion in classes of fifty and under. 

" In nine out of sixteen grades the higher rate of promotion 
at the end of the February- June term, 1911, was in classes of 
fifty and under; in seven the higher rate was in classes of over 
fifty. The rate of promotion was higher in classes of over 
fifty in the 1-B, by .29 of 1 per cent. ; in the 4-B by .59 of 1 per 
cent; in the 5-A by 1.29 per cent; in the 5-B by .09 of 1 per 
cent; in the 6-B by 1.58 per cent; in the 7-B by 3.09 per cent; 
and in the 8-B by 2.18 per cent. But the difference in the rate 
of promotion was either so small or the pupils in the given 
grade were so few that the higher rate of promotion in classes 
above fifty in these seven grades makes a difference of only 134 
promotions. 

'* In each of the grades 1-A — 4-A, — containing 80 per cent of 
all pupils in over-size classes — the rate of promotion, with the 
exception of the 1-B grades, was higher in classes of fifty and 
under. But, with the exception of the 1-A grade, the differences 
in the rate of promotion are too small to affect materially the 
number of promotions. The higher rate for classes of fifty and 
under in the 2-A grade would have increased the number of 
promotions in classes of over fifty by nineteen — the equivalent 
of one additional 2-A promotion to each 386 pupils; in the 2-B 
by seventy-nine — the equivalent of one additional 2-B pro- 
motion to each 104 pupils; in the 3-A grade by fifty-two — the 
equivalent of one additional 3-A promotion to each 139 pupils; 
in the 3-B by forty — the equivalent of one additional 3-B 
promotion to each 167 pupils; and in the 4-A grade by seventy- 
eight — the equivalent of one additional 4-A promotion to each 
sixty-seven pupils. In the 1-A grade, however, the higher rate 
of promotion would have increased the number advanced by 
592 — the equivalent of one additional promotion to each twenty- 



76 Variation in the Achievements of Pupils 

five 1-A pupils in classes of over fifty. The rate of promotion 
in classes of fifty and under was also higher in the 7-A by 6.78 
per cent, and in the 8- A by 7.77 per cent. The number of pupils 
in these grades was, however, small, so that, had the higher rate 
for classes of fifty and under prevailed in classes of over fifty, 
the number of 7-A promotions would have been increased only 
twenty-nine, and the number of 8-A promotions only twenty. 

" Thus, although the higher rate of promotion is found, in 
the majority of grades, in classes of fifty and under, this higher 
rate is so small that, had promotions in each of the several 
grades been the same for classes of over fifty as for classes of 
fifty and under, there would have been, in classes of over fifty, 
a net increase of only 789 promotions out of a total of 73,991 
pupils — the equivalent of one additional promotion to each 
ninety-four pupils in classes of over fifty." 

The most evident conclusion is that promotion rate is probably 
not a measure considered by itself. It must necessarily be an 
inadequate measure because of the probability that it will be 
influenced by administrative policy" and community sentiment. 
If studies of promotion rates are utilized along with other 
measures of progress and measures of attainment they become 
valuable as aids for the interpretation of data. 

25 For an excellent discussion of phases of this problem, see Fifteenth Annual 
Report of the City Superintendent of Schools of New York City, pp. 41-44, 
July 13, 1913. 



CHAPTER VI 

SUMMARY AND SUGGESTED INTERPRETATIONS 
OF THE DATA 

What These Tests Measure ^ 

Aside from studies of the records of the pupils in these tests, 
their variation and the amount of growth by grades, as presented 
in the preceding sections, one large problem of this study has 
been to determine, if possible, the relationship which exists 
between attainment and size of class. So far as the records of 
these tests are valid, there is apparently no relationship between 
the size of class in which the children have been taught during 
the present year and the attainment or variability. Although 
this result is presented for what it is worth on the evidence 
collected, nevertheless, it is in order to suggest reasons for 
this absence of correlation. 

In the first place, possibly these tests do not measure the ability 
of school children in the various subjects tested. Even if they 
did measure the ability and to a sufficiently fine scale that the 
units were comparable with the units of class size, nevertheless, 
the variations among the attainments of the different classes 
are far greater than the variations in the class sizes which would 
suggest at once little possibility of relationship between class 
size and attainment. 2 For example, the average of all the 
class sizes is 35.5, with an A.D. of 5.75, whereas the average of 
all spelling records is 52.5 per cent, with an A.D. of 12.4. The 
sam^ general relationship holds for arithmetic, English composi- 

1 Extended discussion of the relation of time cost, expenditure and amount 
of home study is not made. The facts have been presented in the tables 
merely that anyone who is interested in making comparisons between typical 
attainments, typical time allotments, etc., may have here a tentative stand- 
ard. It will be observed that there are no consistent relations between these 
factors and attainment. In many instances it actually costs less in money 
and time to attain a higher result in the larger classes. 

^Various so-called tests of mental ability, have the same fault; they do 
not seem to correlate, i.e., the status of a pupil in a certain test is likely to be 
very much changed in other tests. 

77 



78 Variation in the Achievements of Pupils 

tion, and range of vocabulary, but does not hold for handwriting 
measured for quality. 

Again there may be something inherent in the groups which 
are tested, which cannot be estimated. It may be that there is 
present some constant error, and that it is impossible to estimate 
what this is, aside from the constant errors which would be pre- 
sent in the ratings of one experienced person. Such a constant 
error should be small for all of the data, as a person experienced 
in making ratings did the rating for all of the classes. The most 
evident conclusion is that we must study these tests far more 
closely and subject our methods of investigation to far sharper 
scrutiny than we have done heretofore, before we claim too much 
for them as measures of ability in these various subjects. 

The tests are designed to measure school work. If upon any- 
thing, they are based on actual school work, and the measure- 
ments are made upon the basis of scales derived from school 
work. The Hillegas and Thorndike scales were made from 
samples of children's work; Buckingham's lists of words were 
derived from school lists and those of Rice; the problems of 
Courtis and the list of words for the range of vocabulary test 
have a like origin. But even with these considerations, we have 
no means of estimating without further experimentation with 
the same children in how far these tests measure complexes of 
school ability and native capacity of the children in these 
subjects, and it is conceivable that these tests may measure 
largely the ability of the teacher to produce results in the 
pupils under her charge. ^ There is evidence throughout the 
study that the ability of the teacher exerts a potent influence 
upon the attainment of the group. In every instance in which 
there is a close approach in attainment of the half years of a 
grade, the teachers of the lower half are equal or superior to 
those in the second half year. In general, the class taught by 
the teacher with the superior rating shows a higher per cent of 
overlapping in all the subjects, irrespective of the size of the 
class. Other evidence of the influence of the ability of the teacher 
is found in the fact that if we compare the attainment of children 

3 The amount of strain which the teacher bears in the larger classes is a 
matter that cannot be estimated on the best evidence obtainable but seems 
to be a variable quantity; many teachers prefer large classes and complain 
little about undue strain. In other instances teachers insist that small 
classes are necessary to relieve over-strain. 



Summary and Interpretations of Data 79 

taught by one teacher with attainment of the children taught 
by the other teachers of a system, we note great differences in 
the amounts of variabiHty. This holds for all subjects except 
handwriting and is one form of evidence that must be taken 
into account. However, this should be corroborated by the 
demonstration of a relatively high coefficient of correlation 
between the attainment of the class and the ability of the 
teacher. Such an extensive problem was not one of the problems 
of this study and our limits would not permit the gathering of 
the large number of ratings for each of the teachers without 
which it is impossible to estimate the amount of this influence. 
On the basis of the ratings gathered, great care has been taken to 
equalize the influence of teaching ability in all instances in which 
conclusions concerning attainment and size of class are ad- 
vanced. Further than this we can at this time only suggest 
the great importance which an extensive study of teaching 
ability holds for educational administration. 

THE USE OF VARIABILITY AS A MEASURE 

The absence of relationship between the variability and size 
of class would not be highly significant were it not for the absence 
of relationship between attainment and size of class'* which the 
records of the various tests indicate. It should be emphasized 
that variability as a measure of efficiency or of anything else is 
to be used with very great caution because without most ex- 
plicit definition it is extremely difficult to know exactly what 
variability measures. The results in this research are sufficient 
to indicate that the presence and great range of variability 
are facts that can be explained only by evidence from many 
sources. The use of variability as a measure by itself cannot be 
regarded as trustworthy. 

Complete summaries of all the data in charts and tables have 

been presented in Chapter III with the suggestion that these 

be used as tentative standards by students who desire to repeat 

the measurements utilized in this study. In addition these 

tables furnish standards for the derivation of better and more 

* The Pearson coefficient between class size and attainment has not been 
computed for any of the cities. It wotdd not be a very significant measure 
because if the grades are all taken together we should have a mixture of 
species; when the grades are separated the number of cases is not sufficient 
to give a reliable measure. 



80 Variation in the Achievements of Pupils 

complete distributions as work of this character is extended. 
Again it is hoped that the method may prove suggestive in 
developing more extensive methods for making surveys of the 
class room work of the elementary school. 

A further analysis of the results indicates in general a lack 
of correlation between the size of class in which the children 
have been taught and such factors as are commonly accepted 
as adequate measures of school work and progress. It is sig- 
nificant, moreover, that the results obtained in this portion of 
the study are in general agreement with every investigation of 
the question of class size that has been carried out in a scien- 
tific manner. 

Yet these results are the opposite of what we might expect 
were we to take as our guide mere opinion. A careful study 
of some one hundred and fifty school reports, and nearly all 
of the surveys that have been made in the past few years, reveals 
the fact that the opinions of supervisors and officers tend to 
be in favor of classes of forty or under. Typical opinions and 
rules of Boards of Education based upon opinion are suggested 
in the following paragraphs: 

'^Distribution of Pupils. In view of the large number of 
pupils to be cared for and the varied conditions that obtain in 
the distribution of the population, the apportionment of pupils 
among teachers was as equitable as circumstance would permit. 
For example, in the fifth month there were twenty-one teachers 
who had over forty-five pupils, ninety who had from forty to 
forty-five, one hundred and thirteen who had thirty-five to 
thirty-nine, and one hundred and fourteen who had thirty to 
thirty-four. 

" The average number of pupils based on total enrollment 
per teacher in the elementary schools was forty, but on the basis 
of the average number belonging it would be reduced to thirty- 
four. In several buildings the average number per teacher is 
necessarily small and this has the effect of lessening appreciably 
the average for the city. For example, in the Jordan, Bonne- 
ville and Lake Breeze schools, which are somewhat isolated, 
effective work can be done only when the average number of 
pupils to the teacher is about twenty. Even under these con- 
ditions the teacher must have two or three different grades in 
her room. The Jordan has forty pupils in six grades, with two 
teachers; the Lake Breeze, twenty pupils in four grades, with 
one teacher; and the Bonneville, ninety pupils in seven grades, 
with four teachers. Then the nature of the work in the Bryant 



Summary and Interpretations of Data 81 

requires a reduced number of pupils for each teacher, the average 
for the thirteen teachers there being but little over that in the 
high school. Again, in the Twelfth school, where we deal with 
atypical children, it is necessary to keep the average under 
twenty. 

** In the kindergarten each teacher had during the year an 
average of fifty-three different children under her charge, but 
the average enrollment for any month did not exceed thirty-five 
for each teacher.^ 

''Classes in the Elementary Schools of Commendable 
Size. The school authorities deserve much credit for keeping up 
with the very rapid increase in school poptdation, which has been 
taking place during the last decade, with an equally rapid ex- 
tension of the school plant and increase in the number of classes, 
with the restdt that all pupils are afforded a full day's schooling, 
and that in classes of very favorable size, in comparison with 
those of most large, rapidly growing cities. While many such 
cities are struggling to give thousands of pupils a full school 
day, and to reduce the size of elementary classes to forty-four, 
forty-two, or forty pupils, as a practical ideal for the immediate 
future, Portland schools are already enjoying the great advan- 
tage of an average membership of scarcely thirty-six. While an 
average membership of thirty is preferable to one of thirty-six, 
the authorities will do well, in the next few years, not to let 
classes increase over the present size." ^ 

*'Sec. 50. First grade classes shall consist at the beginning 
of the school year of at least forty pupils enrolled. Whenever 
the average daily attendance shall fall below thirty-five, the 
Superintendent shall report the fact to the Board, and if in his 
judgment it be advisable, shall recommend a plan for consolida- 
tion or for the formation of a new class. Other primary and 
grammar classes shall consist of at least forty-five pupils enrolled 
at the beginning of the school year, and the Superintendent 
shall likewise report when the average daily attendance falls 
below forty. In schools having less than four classes, these num- 
bers may be modified to meet the needs of classification. In 
classes of the same grade, in any particular school, the number 
of pupils should be kept as nearly equal as possible. 

"Sec. 51. Teachers of mixed first and second grades, shall 
receive first grade pay, providing that their classes have an 
average daily attendance of thirty pupils in the first grade." ^ 

5 Twenty-third Annual Report of Salt Lake City. For the school year 
1912-1913. 

^ Report of the Survey of the Public School System, City of Portland, Ore- 
gon Dec. 27, 1912, p. 124. 

■^ Rules and Regulations of the Board of Education, San Francisco. Adopted, 
Dec. 28. 1910. 



82 Variation in the Achievements of Pupils 

*'Sec. 11. The niimber of teachers to be assigned to any 
school building shall be determined upon the basis of an average 
daily enrollment per month of not less than forty, or more than 
fifty pupils per teacher for graded schools, and not more than 
thirty nor less than twenty-five pupils per teacher for high schools. 
Exceptions may be made in case of schools in remote districts." « 

* 'Regulation 44. Required Daily Attendance. Forty 
pupils, average daily attendance, shall constitute a class. Any 
wide variation from this number is to be explained to the Com- 
mittee on Teachers and Salaries by the Superintendent of 
Schools. "9 

" Whenever the register number of children in a class in an 
elementary school, excepting open-air classes, ungraded classes, 
and classes for blind, deaf, truant, or crippled children, falls 
below thirty or rises above fifty, the principal or teacher in 
charge shall notify the District Superintendent, who shall report 
to the City Superintendent of Schools the steps that should be 
taken, by consolidation of classes, transfer of pupils, or other 
means to secure an economical distribution of teachers and 
pupils (As amended May 14, 1913). "i" 

" No grammar grade shall have less than forty pupils, except 
in the eighth grade, where the minimum shall be thirty, except 
by permission of the committee on instruction and educational 
supplies." 11 

As contrasted with these opinions we have other opinions 
from supervisory officers of equal competence : 

" It may be that better results are not obtained with small 
classes because the teachers have become so accustomed to 
dealing with the larger classes that they are not able to adjust 
themselves and adapt their methods to it, when they meet the 
small class. Some evidence in favor of this view is found in 
the preference held by many teachers for classes in the forties. 
* I feel as if I do not have enough to work upon in a class of 
thirty,' is the way this preference is often given expression. "^^^ 

The superintendent of schools for Newark, New Jersey, 
suggests that ** The manual and craft studies will not admit 

8 Rules and Regulations and Course of Study, Minneapolis Public Schools, 
1910-1911, p. 12, Sec. II. 

^ Rules of the Board of Education of the School District of the City of Cin- 
cinnati, adopted, April 17, 1905, p. 83. 

10 Manual of the Board of Education, City of New York, 1914, 

11 Newark, N. J., Board of Education, Fifty-fourth Annual Report for the 
school year ending June 30, 1910, p. 293. 

Compare with these quotations the elaborate schedules for the assign- 
ment of class sizes in Report of the School Committee, Boston, Mass., 1910, 
p. 72, Sec. 292. 

12 The Psychological Clinic, Vol. Ill, No. 7, p. 211. 



Summary and Interpretations of Data 83 

so large a class as from thirty-five to forty." In the same sec- 
tion of the report, he recommended that ** Although no specific 
rule can be laid down as to the size of the class, there is a general 
rule that a class of say thirty-five to forty pupils on the average 
can be handled efficiently by most teachers." In other sections 
of the same report, he recommended that ** The cost of high 
school maintenance be reduced by reducing the number of teach- 
ers and increasing the size of the classes." i' 

It is needless to multiply opinions. Accumulating a vast 
array of opinions leads us no nearer the solution of a problem. 
But when we have a body of data taken with the great care 
that has been used in gathering the results in the present study, 
we at least have a basis for analysis in the light of our best 
knowledge, and may suggest helpful interpretations that take 
into account all of the factors so far as we are able to estimate 
them. 

It is unnecessary to review the evolution of the various types 
of schools and types of teaching. These facts may be gleaned 
from any of the authoritative treatises on the history of educa- 
tion. i< Prior to the eighteenth century, school instruction 
ranged from tutorial instruction to instruction in classes of 
large size in schools of elementary and secondary grade. In 
the schools of the Port Royalists in the seventeenth century 
a definite attempt to organize schools with very small classes 
appears. In the latter part of the eighteenth century, and in 
the early part of the nineteenth, there was ushered in a period 
of provision for education, upon a more extensive scale than had 
hitherto been attempted. The Sunday School movement, the 
Infant Schools, and the Monitorial Schools introduced in a 
peculiar way new problems of class teaching. The problem was 
largely one of administration, and required the handling of 
groups of children by a teacher or master and assistants. This 
problem developed until the ideal in the Lancasterian system 
was to have a teacher with a large number of monitors, in 
charge of the instruction of one thousand pupils. 

The wide introduction of the monitorial system in the United 
States tended to establish a policy of large classes, particularly 

" Annual Report of the Superintendent of Schools, Newark, N. J., 1912. 

" Readers are referred to such standard works on the History of Education 
as those by Monroe and Grayes, and also the Encyclopedia of Education, 
8dited by Paul Monroe, and similar treatises. 



84 Variation in the Achievements oj Pupils 

in the lower grades. Thus with the passing of the system there 
was left no considerable discontent with large classes. The 
persistence of the ideal of organization is still found in such 
cities as New York, where to-day a number of buildings are 
in use, whose construction and interior arrangement follows the 
pattern suggested by the monitorial schools of an earlier day. 
The popularization of education, the enactment of compul- 
sory attendance laws, and the increase in the density of popu- 
lation, have increased the school attendance in the majority of 
communities at such a rate that provisions for schools have 
not kept pace, and this has tended to reinforce the existing 
tradition in favor of large classes. Again the enrichment of 
the curriculum, the increase in expensive buildings and equip- 
ment, the addition of special schools, have all tended to make 
the reduction of the size of classes a difficult matter, and to 
accentuate its importance as a problem in American school 
administration. In the upper grades, a counter force appears 
in the form of elimination which tends to reduce the number 
of pupils per teacher. The fact is abundantly illustrated in 
the tabulations by classes and grades in any city report. Un- 
fortunately it is a condition found in nearly all of the growing 
cities of the United States. 

The relatively large groups of children that are marshalled 
for instruction have caused, for many years, the presence of 
large classes in our elementary schools, and the necessity of 
devising means by which to cope successfully with the problems 
of mass teaching has tended to evolve a type or pattern of 
teaching which has become established in American teaching 
and supervision. Even in the smaller classes in the higher 
grades, where the more rigid ideals of grading and elimination 
have reduced the number of pupils per teacher, the conven- 
tionalized methods of teaching have been the same. Probably 
the fact that teachers in the upper grades are drawn largely 
from the experienced teachers of the lower grades has contrib- 
uted to this condition. Teachers do not distinctively change 
their methods of instruction when they have smaller classes. 
The testimony of progressive supervisors bears witness to the 
fact that it is very difficult to get teachers to do much 
individual teaching even when they have small classes. This 
is corroborated, moreover, by the fact that many teachers 



Summary and Interpretations of Data 85 

actually prefer classes of about forty for here they do not feel 
the pressure to combine individual teaching with group teach- 
ing. In his study of promotion rates and class size Cornman 
suggests : 

"Again it may be that the pupil does not reap the advantages 
supposed to accrue to him in small classes unless the class be- 
comes so small that the teacher may direct a large share of 
attention to the study of the individual peculiarities of her 
pupils and to the employment of special methods in each child's 
behalf. The possibility of realizing these conditions is found 
only in the 'special class' of from fifteen to twenty-five pupils. 
As was said editorially in a former number of The Psychological 
Clinic, * The grade teacher is interested in teaching reading, 
writing and arithmetic. The special teacher must be interested 
in developing the individual child. ... In the grades 
attention must ever be centered upon the curriculum, pedagog- 
ical methods and the result as shown through class promotions. 
There is a problem of mass instruction, and there is an entirely 
different problem of individual development. These should be 
kept separate and distinct, and the public schools should never 
give up the older ideals of mass instruction. Clinical psychology 
and the special teacher will not supplant the more general 
features of the public schools; they will only supplement what 
is already to be found in the schools, in order to make the work 
effective in meeting special conditions.' The cost of reducing 
regular classes to an average size of even thirty pupils would 
be so great as to be practically prohibitive, so that the public 
schools could not give up the older ideals of mass instruction. 
Perhaps the most economical, as well as most effective, solu- 
tion of the problem is the maintenance of regular classes of 
medium size — between forty and fifty pupils — the gradation of 
which classes shall have been greatly improved by transferring 
from them to special classes — fifteen to twenty-five in member- 
ship — for individual pedagogical treatment of all pupils who 
seriously deviate in their physical, mental, or moral character- 
istics from the average or normal child." ^^ 

Under recent demand for small classes so that there may 
be more individual teaching, the conventional mass teaching 
tends to be the type. The analysis of the conditions as cited 

" Psychological Clinic, Vol. Ill, No. 7, pp. 211-212. 



86 Variation in the Achievements of Pupils 

above for the city of Philadelphia by so competent an inves- 
tigator as Dr. Cornman bears witness to this fact. The 
fact that classes of twenty-five or thirty do no better than those 
of forty or fifty does not indicate that all classes should be made 
larger in the interest of public economy. One class among 
those studied in this report is a special class in which there is 
a large amount of individual teaching, and in this the results 
are such as to indicate the possibility of getting higher attain- 
ment with a selected group of pupils in charge of an excep- 
tional teacher, who introduces a large amount of individual 
teaching. Such conditions are duplicated throughout the United 
States in many experimental and special situations. The 
problems of mass instruction for the great majority of chil- 
dren, however, belong in an entirely different category. The 
results presented in this study indicate that instead of making 
all classes larger in the interest of public economy, on the con- 
trary, two policies must be pursued: 

1. That new standards of individual adjustment to teaching 
and supervision shall supplant in part present class or mass 
methods of teaching as an ideal. 

2. That the size of classes in the elementary school shall be 
reduced to numbers smaller than what may become a desirable 
norm, in order that teachers may be freed from the conditions 
which have produced a traditionalized mass teaching, and thus 
be given an opportunity to develop the new type of teaching 
in classes which shall take account of individual differences. 

On the other hand, it must not be assumed that classes can 
be indefinitely reduced with increasing efficiency in instruction. 
If such were the case, the instruction of a single child by a 
tutor would give a most competent education. It would be 
better than school education. Such an assumption leaves out 
of account all the incidental instruction that a pupil gets from 
his fellows, all the concrete social experience of adjusting him- 
self to the group life — a thing that makes him another individ- 
ual, — in short, all the stimulus that comes from contact with 
others. 

In recent years researches in social psychology have estab- 
lished several truths which find their application in the group 
life of the school, and in the performance of children in groups 
of various sizes. In the first place, the results of Schmidt, 



Summary and Interpretations of Data 87 

Mayer, Meuman, Triplett, and Fere indicate that people work- 
ing in groups do far better than persons working alone. The 
results of Meuman show particularly that as the group increases 
in size, the accuracy and amount of work increase. Mayer 
and Meuman, by measuring the effects of distractions, have 
both shown that attention is stronger in the group than in 
the individual. 16 

This dynamogenici' effect of various social factors, one of 
the most important of which is the size of the group, upon the 
performance of individuals, is a matter much neglected in school 
work. The results in the present study indicate the influence 
of this factor, and emphasize the fact that the r61e it should 
play, and the amount of influence it should have, are among 
the important problems in the assignment of class size. This 
implies that the desired condition in instruction is one where 
the group is small enough to enable the teacher to give adequate 
personal attention to the pupil and yet large enough to pro- 
vide all the important influences which come from working in 
groups. How large then should this group be ? 

The fact that school attendance tends to be better in the 
larger groups in the cities examined and in certain of the schools 
of New York City indicates that children like to be with a 
crowd, 18 as well as affirms the fact of the dynamogenic influence, 
but does not argue that we should determine the size of classes 
by this single measure. ^^ Capacity for individual learning is 
doubtless a far better characteristic for a class to possess than 
almost perfect attendance. Besides one may get attendance in 
other ways, as by more interesting and vital teaching which 
will result from the training of teachers in this direction and 
from such assignments of class size as will permit the use of 
individual teaching. There are no data upon which to base a 

" For a summary of these studies in Social Psychology, see Science, New 
Series, Vol. 31, No. 803, pp. 761 to 767. Pedagogical Seminary, June, 1905, 
pp. 214 to 230. See also Bibliography, pp. 229-230. Physiological Psychology 
by Ladd & Woodworth, pp. 532-533. See also the references cited in foot- 
notes of these pages. Pedagogical Seminary, Vol. 7, No. 1, p. 13 S. 

" Other types of dynamogenesis are illustrated in Thomas's Source Book of 
Social Origins, p. 618 ff. 

18 Hall, Adolescence, Vol. II, Chapter XV. 
Thorndike, Educational Psychology, Vol. I, Chapter VII. 
MacDougall, Social Psychology. 

1* There may be a fallacy in this measure taken alone, for the condition may 
be influenced by pressure put on at school and at home, which compels the 
child to keep his place in school. 



88 Variation in the Achievements of Pupils 

final prescription. We need a large amount of experimental 
work upon these various factors. If the present investigation 
points to anything, it indicates a serious condition in American 
teaching and supervision. 

Recent careful studies of the physiology of children and of 
school hygiene indicate that no class properly seated may be 
larger than fifty. Dresslar, one of the most competent inves- 
tigators, 20 in stunmarizing all of the researches made on this 
question, and the results of his own studies, suggests that classes 
may not economically be made much larger than forty to forty- 
five. The present investigation indicates the general lack of 
relationship between the size of classes as organized in the situ- 
ations studied and the attainment reached in the subjects tested. 
The study most emphatically does not indicate that we should 
increase classes even to the extreme limits reported. The lack 
of relationship which is evident suggests a stupendous problem. 

The optimum size for the most efficient instruction cannot 
be determined by the evidence at hand. Experimentation and 
further study are needed. We can only indicate certain general 
facts about the situation. At one extreme, tutorial instruction 
of the individual is undesirable because the social or group 
influences of education are absent. On the other hand, instruc- 
tion in classes above fifty is absolutely undesirable because of 
physiological effects. Merely to reduce the size of the classes 
without changing the traditional method of teaching is not to 
add to efficiency in instruction. This is exactly what is being 
done in many of the current experiments in this country, and 
by the expressed opinions of many school men. 

The evidence from the investigations of Dr. Rice^i and his 
analysis of the bearings of these in American school practice 
give added force to these contentions. Dr. Rice makes clear 
that no one knows the amount of influence exerted by such 
factors as the age, nationality, heredity, and environment of 

20Bulletinof the United States Bureau of Education, 1910, No. 5, p. 17 ff. 
School Hygiene, 1913, pp. 30-37, and pp. 57-73. In this connection such enact- 
ments relating to ventilation as have been passed by the legislatures of New 
York, Massachusetts, and Pennsylvania, are suggestive. See also Building 
Code of the State Board of Education of New Jersey, 1913. 

21 Educational Research— A Test in Arithmetic, The Forum, Vol. XXXIV, 
No. 3. The Futility of the SpelHng Grind, The Forum, Vol. XXIII, Nos. 
2 and 4. A Test in Language, The Forum, Vol. XXXV, No. 2. Language 
(continued) : The Need of a New Basis in Education, Vol. XXXV, No. 3, 
p. 44 ff. 



Summary and Interpretations of Data 89 

the pupils, the training and personality of the teacher, the 
methods of instruction or the like. These conclusions of Dr. 
Rice are held by competent students of education to-day, 
although the work of Thorndike and others is giving us answers to 
some of the elements of these elusive problems of education." 
The present study indicates that we can probably not determine 
the precise influence of class size because of its complex inter- 
relations with other factors, the amount and influence of which 
we are yet not able to estimate and eliminate by means of our 
present methods of measurement. 

A careful perusal of the arguments of Dr. Rice and an exami- 
nation of his data indicate that probably the attainment of 
children in school work represents very largely the ability of 
the children in things which they have worked out 2 3 or in the 
language of the modern psychologist, " the things to which 
they have reacted." Psychology presents much evidence to 
indicate that there is no learning of consequence which does 
not result from the "varied reaction" of the learner. Merely to 
"put through" the mind of the child as he deals with the material 
to be learned, is of little more consequence in human learning^* 
than attempts to teach an animal an act by "putting it through" 
the various steps of that act. This is only another way of 
saying that the most economical learning will result from the 
economical arrangement of situations to which the pupil shall 
react. In the last analysis our school work must depend in 
large part upon the arrangement of situations and the securing 
of proper responses in the most economical manner. Dr. Rice's 
suggestion that the high probability that this depends largely 
upon the power of the teacher is only a half truth. The power 
of the teacher, aside from the influence of personality, will be 
manifested largely in the marshalling of situations in such a 
way as to bring about desirable responses. But there are other 
factors which may be brought into account, which will compel 
reaction on the part of the pupil and which may thus contribute 
very largely to securing optimum conditions for learning in 

22 Such studies as The Elimination of Pupils in the High Schools of New 
York City, by Van Denburg, give us important answers to certain problems. 

23 The Forum, Vol. XXIII, p. 415. 

2^Ladd & Woodworth — Physiological Psychology, Chapter VIII. See 
also A Study in Incidental Memory by Garry C. Myers, Columbia Univer- 
sity Contributions to Philosophy and Psychology, Vol. XXI, No. 4. Thorn- 
dike, Educational Psychology, Vol. II, Chapters I-IV. 



90 Variation in the Achievements of Pupils 

ways that are outside the control of the teacher. Such things 
are the group stimulus, and various other stimuli which are 
not consciously the result of the teacher's work in arranging 
situations and responses. Only a careful study of these separate 
factors, an estimation of their probable effect, and the resultant 
arrangement in proper combination can be expected to solve 
many of these important problems. 

These considerations suggest that two definite things must 
be done at one and the same time: 

First, the classes must be made smaller so as to make indi- 
vidual teaching physically and psychologically possible. The 
experience in the organization of classes of exceptional children 
in England, Germany, and the United States indicates that the 
limits are roughly ten and twenty-five. 25 Experiments carried 
on with normal children and exceptional children in this country, 
utilize in general class sizes within these limits. However, 
experimentation may show that these are not optimum limits. 
These limits which have been prescribed by law in some in- 
stances, and frequently by boards of education, 2 e are not the 
result of experiment, but are rather" the approval of certain 
types of practice that have been guessed at as satisfactory. 

Second, the teacher must couple individual teaching with 
group teaching. It is incumbent upon supervisors to derive 
standards for individual teaching and to assist teachers in 
applying these in the group. Exactly what size this group must 
be in order to secure the optimum results cannot be determined 
from the evidence in this study, and it is doubtful whether it 
can be determined at present from any array of evidence col- 
lected in American schools, because there is not enough practice 
of individual teaching, either as a major method, or as a method 
of co-ordinate importance with methods of mass teaching in 
American schoolrooms to give us after the most painstaking 
collection of data, these needed facts: 

First, how small must classes be so that the teacher can 
determine the individual needs of each member ? 



25 Bulletin of the United States Bureau of Education, 1911, No. 14. Red 
Codes of N. U. T. for 1908-1912. Bulletin of the United States Bureau of 
Education, 1907, No. 3. 

26 Laws of New Jersey, 1911, Article X. See also Manuals of Board of 
Education, New York City, 1911 and 1914, for sample provisions in the 
United States. 



Summary and Interpretations of Data 9 1 

Second, how many must be in the group before the maximum 
of social stimulation is reached ? 

Third, if maximum control, and maximum stimulation of the 
individual require a different sized group than that now gener- 
ally organized, what size offers an opportunity for the optimum 
combination of these factors ? No one knows. The question 
can be answered only by a large amount of experimentation, 
for a study of situations in which all of the factors are not 
taken into account can do no more than establish the inade- 
quacy of present procedure, or summarize a practice whose 
value may be far below that which carefully conducted experi- 
ments extending over several years or better through the entire 
elementary school Hfe of a group of individuals indicate to be 
desirable. 



APPENDIX I 

GENERAL DIRECTIONS FOR THE ADMINISTRATION 
OF THE TESTS 

1. In general, the investigator should provide uniform ruled 
paper similar to that used for composition work in the several 
systems to be tested for the tests in composition, handwriting 
and spelling. He should also provide a supply of pens of the 
kind the children are accustomed to using. 

2. For the timing a good stop watch is desirable although not 
necessary. A good ordinary watch should be sufficiently accu- 
rate. 

3. Use large envelopes about 10| x 12 inches. 

4. Write on the outside of the envelope the following facts in 
order : 

a. Name of City. 

b. Name of building. 

c. Grade. 

d. Name of teacher. 

e. Average daily attendance. 

f. Time of day of test, i.e., time of beginning of test and time 

of ending of test. 

g. Date of test. 

Directions for the Administration of the Spelling 

Test 

Upon entering the classroom obtain from the teacher a sufficient 
amount of ruled paper such as is used for ordinary composition 
work, to supply each pupil with one sheet. ^ Ask the regular 
monitors to distribute one sheet to each pupil. Then give these 
directions: '' Write your name in the upper right-hand corner 
of the sheet. Under this state whether you are a boy or a girl. 
Under this write the date of your birthday. Under this write 
the number of years old you were at your last birthday. 

" I wish you to write carefully some sentences which I shall 
dictate. Number them in order on the left." 

In dictating these sentences read each one through twice, 
then at the signal, ** Write," dictate the sentence in phrases as 
marked and allow the number of seconds indicated above each 
phrase for writing that phrase. 

1 Or supply the pupils with the uniform paper furnished by the investigator. 

92 



Appendix I 



93 



SPELLING TEST2 

To test grade IV, dictate sentences, 1, 2, 3, 4, 5, 6; grade V, 
sentences niimbered 3, 4, 5, 6, 7, 8; grade VI, sentences num- 
bered 5, 6, 7, 8, 9, 10; grade VII, sentences numbered 7, 8, 9, 10, 
11.12. 



Ill 



IV 



V 



VI 



VII 



VIII 



IX 



10" 

forty men. 
10" 
in jront of me. 
10" 
a white button. 

nr 

the surface of the water. 

12" 
is too loose. 



10" 

1. I will send^ 

10" 

2. Please pass 

10" 

3. He likes to wear 

4. The rope can just touch 
^ 12" 

5. I believe that your belt 

ur 

6. They drove to the circus m a carnage. 
^ 12i" ^ 12|" 

7. He laughs and is saucy \ and keeps on whistling. 

15" 15" 

8. They may fail in the beginning\hut soon they will succeed. 



10" 



10" 

he slipped. 



9. While ascending the stairs 

15" I ^ 15" 

10. You cannot imagine a person I with so bad a character. 



12i" 



11. He made a peculiar mixture 

10" 

12. The intelligent scholars 



of ashes and cement. 
10" 10" 

were all present on this occasion. 
18" 
that this girl is thoroughly conscientious 
15" 
and will never disappoint you. 



15 

13. I can guarantee 



10" 



When the last sentence has been dictated, and time allowed for 
writing the last phrase, give this signal: "AH stop. Pens down. 
Blot your work. Monitors collect." 

Fasten the papers together, and place them in a large envelope. 
On the outside of this envelope, record the facts indicated under 
General Directions. 



2 The time for writing the sentences in this spelling test was standardized 
by dictating them to several hundred children. By means of a stop watch 
the time necessary to write each of the phrases was determined. These 
tentative standards were utilized throughout the study in order to make the 
results closely comparable. 

3 The words in itaHcs are the standard words for each of the grades. 



94 Variation in the Achievements of Pupils 

Directions for Administering the Composition Test 

Upon entering the classroom obtain from the teacher a supply 
of paper such as is used in the regular composition work or use 
the uniform ruled paper you have selected for the testing. Have 
one sheet distributed to each pupil. Ask the pupils to prepare 
the paper in the same manner as indicated for the spelling test. 
Then, " Pens down." 

Then say: '* To-day I am anxious to have you write me a 
good story. I shall write a subject on the board and I want you 
to tell me the most interesting story you can. After you begin 
(and do not begin until I say ** Go,") you are not to consult the 
dictionary nor to ask questions of anyone, not even your teacher. 
After I write the subject on the board you may ask me questions 
for a few minutes." 

Then write on the board this subject: ** How I would spend 
one hundred dollars to please five persons who like different 
things." Allow three to five minutes for questions which when 
answered give a clear understanding of what is wanted. Elim- 
inate all others. 

Then say, ** Go," and allow the class to write twenty-two 
minutes. At the end of that time, "All stop. Pens down. 
You will now have a few minutes to look over your paper. 
Look through it carefully and make any corrections you wish 
without consulting anyone." 

Allow three minutes for this, then, ** Pens down. Blot your 
papers. Monitors collect." 

Mark the set as indicated under the spelling directions. 

Directions for the Tests in Handwriting 

1. Use a ruled paper similar to that used in the systems 
tested. Where the school authorities are willing to furnish 
the paper the regular paper used for penmanship or composition 
may be used. 

It is desirable that the investigator provide the pupils with 
clean pens of the kind used in the system. 

2. Upon entering the classroom determine from the teacher 
what piece of poetry or prose containing thirty or more words 
has been memorized by the pupils. Often the investigator will 
find that different groups know different passages best. In 
that case allow each group to use what it knows best in the pre- 
liminary test. In tests II, III and IV it is well to attempt to 
confine the writing to two different passages, preferably one, 
because of the difficulty in getting the passages on the board 
as noted below. 

3. Utilizing the regular monitors distribute one sheet of paper 
per pupil and pens in holders to the class. See to it that all are 
supplied with ink and blotters. 



Appendix I 95 

4. Have the class prepare this sheet by writing name, birthday, 
age and sex as indicated under the SpelHng Test. 

5. Test I. Preliminary Test. Have the pupils write the 
first stanza of the passage selected over and over from memory 
in exactly two minutes. While the class is writing record the 
names of any who do not remember the passage. Stop the 
writing at the end of that time, collect the papers, fasten them 
together, label as indicated for the other tests, and in addition, 
mark them, Preliminary, 120 seconds. 

6. Test II. Careful Writing Test. Have the teacher write 
the stanza on the board. If there are two or three groups the 
investigator should write one or more of the passages on the 
board, thus assisting the teacher and saving time. Tell the 
pupils that you are anxious to see how well they can write. Tell 
them to write the first stanza over and over as carefully and as 
well as they can in the time allowed. Tell them to look at the 
board if they forget the passage. Start them on signal and 
allow exactly four minutes. Collect and label as indicated 
under (5) and put on additional label: Careful, 240 seconds. 

7. Test III. Writing Done at the Usual Rate of Writing. Tell 
the pupils that you wish now to see how they write when they 
write about as rapidly as they ordinarily do. Give the same 
directions for the writing as indicated under (6) . Start them on 
signal and allow exactly four minutes. Collect and label as 
indicated above. Additional label, Ordinary, 240 seconds. 

8. Test IV. Speed Writing. " Now let us see how well you 
can write when you write very rapidly." 

Distribute paper as before. ** When I say ' Go,' take your 
pens and write the stanza over and over until I say * Stop.' 
Remember, write as rapidly as you can and still write well." 

Proceed as in Test III and allow four minutes. Label in 
addition. Speed, 240 seconds. 



Directions for Giving the Tests in Range of 
Vocabulary 

1. Distribute the test sheet numbered I and ask the monitors 
to place the sheet face down. See that the class is supplied 
with pencils. Then say: "At the signal, ' Go,' I wish you to turn 
this sheet up, read carefully what it says near the top and then 
do exactly what it tells you. Ask no questions. All ready. 
Go." 

2. Allow three minutes for the test. Note any pupils that 
are unable to go ahead. Tell them individually to read what it 
says and do what it tells them. 

3. At the end of three minutes, "All stop. Pencils down. 
Write your names below the work. Monitors collect." 



96 Variation in the Achievements of Pupils 

4. If desired, the same facts with reference to age and sex 
as indicated in the spelling test may be recorded on this and 
the other sheets. This is not necessary if it has been done on 
one of the other test papers. 

5. In the same manner distribute the test sheet numbered II 
Then say: *' This sheet is similar to the one you have marked. 
At the signal, 'Go,' turn it over, read and do exactly what it 
says as quickly as you can." 

6. Allow exactly three minutes. Stop the work and collect 
as indicated under (3). 

7. In the same manner distribute the test sheet numbered 
III. Give the same directions as noted under (5). 

8. Allow exactly five minutes. Stop the work and collect 
as indicated under (3). 

TEST I 

Write the letter a under every word that is the name of an 
animal. Write the letter t under every word that means a 
kind of tree or wood. Write the letter b under every word that 
means some kind of a book. Write the letter g under every 
word that means some kind of a game. 

Remember — a, for animals 
t, for tree 
b, for books 
g, for games 

lion, tiger, pine, bible, oak, base-ball, primer, tag, deer, 

maple, snake, elm, willow, walrus, leopard, jack-straws, 

birch, tennis, giraffe, hickory, elephant, kangaroo, dictionary, 

dominoes, hemlock, croquet, gorilla, golf, novel, mahogany, 

walnut, encyclopedia, ledger, rhinoceros, parchesi, cypress. 



Appendix I 97 

TEST II 

Write the letter c under every word that means a color. 
Write the letter m under every word that means a thing that 
makes music. Write the letter w under every word that means 
some thing that boys or girls wear. Write the letter d under 
every word that means some thing that a boy can do. 

Remember — c, for colors 

m, for things that make music 
w, for things to wear 
d, for things boys can do 

red, green, guitar, hat, coat, run, work, play, shoe, jump, hide, 

piano, pink, cuff, shout, study, organ, reach, yellow, grasp, 

scream, collar, request, shiver, crawl, shirt, violin, violet, 

disagree, purple, inquire, scarlet, harp, flute, trumpet, practice, 

ramble, crimson, cornet, apron, mandolin, trespass, prevaricate-; 

sweater, confess, ribbons. 



98 Variation in the Achievements of Pupils 

TEST III 

Write a letter g under every word that means something 
good for a boy or girl to be. Write a letter b under every 
word that means something bad to be. Write a letter s under 
every word that means something to do with school. Write 
a letter t under every word like " now " or " when " or " before " 
that means something to do with time. 

Remember — g, for good things 
b, for bad things 
s, for words about school 
t, for words about time 

liar, fair, lesson, then, lazy, steal, teacher, honest, clean, kind, 

never, writing, sneak, reading, polite, before, useful, stingy, 

murder, spelling, arithmetic, cowardly, cruel, afterward, 

whenever, truthful, modest, upright, geography, graduate, 

recess, rascal, drunkard, obliging, later, deceitful, during, 

scoundrel, promotion, grade, generous, criminal, torture, loyal, 

history, miser, reprobate, earlier, courteous, penmanship, 

merciful, forger, courageous, craven, renegade, poltroon, 

reasonable, examination, considerate, deportment, discipline, 

defaulter, equitable, sycophant, preceding, philanthropic, 

hitherto, grammar, etymology, pretentious. 

Directions for the Administration of the Test 
IN Arithmetic 

For the reasons cited in Chapter II, page 15, Test No. 7, 
Series A, of the Courtis tests was selected. The method of 
administering the test and the methods of scoring are identical 
with those used by Mr. Courtis, which have been described 
by him at length. ^ 

* Directions for giving the Courtis tests, 1913. Final Report of the Com- 
mittee on School Inquiry for New York City; 1911-1913, Vol. I pp. 397-546. 



APPENDIX II 
SAMPLES OF TESTSi GIVEN IN SYSTEMS H AND I 

REPRODUCTION STORY 

Will the principals please give this story in grades three and 
four, sending the papers to the office as usual ? The title may- 
be placed on the board. No questions are to be answered and 
the story is to be read but once, distinctly. 

Superintendent. 



The Owl and the Grasshopper* 

A great white owl was sitting one day on her perch in a hollow 
tree. She was trying to get her afternoon nap. But a noisy 
grasshopper sang his song over and over again. The owl could 
not sleep. Finally the owl said, " Won't you keep quiet or else 
go away ? I want to take a nap." But the grasshopper said, 
" I have as much right to sing as you have to sleep. Besides, 
you have never done anything for me." Soon the owl called 
out to the grasshopper, " Well, you have really a beautiful 
voice. Now that I am awake I don't wonder that you love 
to sing. Won't you let me offer you some of the delicious 
honey that I have here ? " The silly grasshopper at once 
jumped up into the tree. The owl caught him in her sharp claws 
and then finished her nap in peace. 

reproduction story 

To be read by the principal in grades five, seven and eight, 
once only, and no questions answered. Aicha and Algeria 
should be written on the board. Papers to be marked with name 
of teacher, school and grade, and sent to the office as usual. 



Superintendent. 

* For the method of scoring these tests, see The Psychological Clinic, Vol. 
VI, No. 1 (March 15, 1912) pp. 1-12. 

' All of the stories have not been reproduced. The " School of Stanz " is 
the original story used by Dr. Rice in his study of attainment in language. 
For text, see The Forum, Vol. XXXV, No. 2, p. 290. 

99 



100 Variation in the Achievements of Pupils 

The Trick of Old Aicha 

Long ago a city in Algeria was besieged by a great army 
and the inhabitants were reduced to the last extremity. The 
mayor called together all the people and said: ** My friends, 
we shall have to surrender the city. We have nothing to eat." 
" No, no," cried an old woman named Aicha. ** Do not give 
up the city. I am sure that the army will go soon. Do what 
I tell you, and I promise you that the city will be saved." The 
mayor consented and the old woman said: "First, we must 
get a cow." *'A cow," said he. " It will be impossible to find 
a single cow in all the city. All the animals have been killed 
long ago." The old woman insisted, and, after a long search, 
they found a cow at a house of an old miser who had hoped 
to sell it some day for a large sum of money. The mayor took 
away the cow in spite of the miser's objections. 

" Now," said the old woman, ** I must have some grain." 
*' It is impossible to find any grain in this whole city," answered 
the mayor. But little by little they collected enough to fill a 
measure and brought it to the old woman. She ground it and 
gave it to the cow to eat. The mayor exclaimed: "Oh, you 
are giving this good grain to an animal when so many people 
are dying of hunger." The old woman said: "Only wait a 
little. The enemy will go away." Then she drove the cow out 
of the gate of the city and it stayed near there, eating grass. 
Some of the soldiers of the enemy came up, seized the cow, and 
led it to their camp. When their king heard where they found 
it, he cried: "Surely, the people in the city cannot be without 
food, as I thought, for if they were hungry they would have 
eaten this cow. They must have more food then we. It is 
long since we had any fresh meat. Well, kill this animal and 
you shall have a good dinner." 

But when the soldiers killed the cow, to their surprise they 
found a quantity of grain in her stomach. The king said: " If 
those people have enough grain to feed their animals they are 
better off than we. We shall die of hunger before they do. 
It is useless for us to wait for the city to surrender." So the 
king marched away with his army and the city was saved. 

The grateful people carried the old Aicha in a triumphal 
procession all around the city and gave her so much money that 
she lived in comfort all the rest of her life. 



Appendix II 101 

Cornelia's Jewels 

Once upon a time many long years ago there lived a lovely 
lady. Her name was Cornelia, and her home was in the great 
city of Rome. Cornelia had two little sons whom she loved 
very tenderly; and the boys, on their part, were very fond of 
their beautiful mother. One day a lady came to call upon 
Cornelia. She was dressed very richly in silk and velvet. 
Around her neck were heavy gold chains, in her hair were 
shining rubies and diamonds. Her fingers sparkled with ex- 
pensive rings. She brought with her a wonderful jewel-box in 
which were other chains and rings and precious stones of every 
kind. 

All these things the lady showed to Cornelia, who admired 
them very much. When the last jewel had been put back into 
the box, the visitor said, " I have shown you all my treasures. 
Where are yours ? Pray let me see them." 

At this moment Cornelia's little sons came running home 
from school. Holding them fast in her arms, Cornelia said 
proudly, ** These are my riches. While I have them, I do not 
need either gold or jewels. They are the most precious treasures 
in Rome or in all the world." 

grade 3. reproduction 
Dick's Cat 

Dick's bed was in an attic. At night many rats and mice 
came through holes in the floor and made so much noise that 
he could not sleep. 

One day he saw a girl with a cat. " I will give you a cent 
for your cat," he said. The girl took the cent and gave Dick 
the cat. 

He took it home. Soon there was not a rat nor a mouse 
left in the attic. Then Dick could sleep well every night. 

GRADES 3 AND 4. REPRODUCTION 

The Two Goats 
Two goats met in the middle of a bridge. It was only wide 
enough for one to cross over at a time. Neither goat was willing 
to go back and let his friend pass by. They began to fight and 
both of them tumbled into the water below. Their wetting 
taught them better manners. 



102 Variation in the Achievements of Pupils 

GRADE 4. REPRODUCTION 

Two Men and the Bear 

Two men once said they would travel together and help 
each other. They had not gone far before they saw a great bear. 

One of the men said, " Together we can kill it." But the 
other man ran and climbed a small tree. The first man had 
now no time to get away. What did he do ? Why, he fell 
upon his face. He lay still, as if he were dead. It is said that 
a bear will not eat a dead man. 

The great bear came up and smelled the man. But he lay 
quite still. So it left him and went away. 

Then the other man came down from the tree. " My friend,'* 
he said, ** the bear seemed to whisper in your ear. What did 
it say to you ? " 

" It gave me some good advice," said the man. " It told 
me never to travel with one who leaves me when danger comes." 

Grade V. Spelling Test^ 

1. My daughter is eighteen years old. 

2. On her journey she saw many cities and islands. 

3. The canoe was huilt roughly. 

4. Surely the grocer has fruit of some kind in that barrel. 

5. Perhaps he has molasses in it. 

6. Those women find it icy walking. 

7. They who do mischief get into trouble. 

8. Tie your handkerchief around your thumb. 

9. I promise to bring knives and leather for the work. 
10. The rabbit ran against the fence. 

Marked on italic words. They are from lists of previous 
years. 

Grade IV. Spelling Test 

Where did the robin build its nest ? 

He made it in the apple tree away from the house. 

The robins were afraid of our children, but they would not 

hurt the birds. 

1 Unfortunately it is impossible to give the relative difficulty of the various 
words used in the spelling tests presented here because all of these words 
have not been evaluated. Roughly those for Grade V as determined by 
Buckingham represent approximately fifth grade ability; the words for the 
other grades are relatively too easy. 



Appendix II 103 

Tom, the cat, is the one who likes birds for his supper. 

Their nest was made of sticks and grass. 

Perhaps there will be as many as four young robins in it. 

Grade III. Spelling Test 

My sister had a cent. She went to buy some candy. What 
did she get ? The man gave her five candy balls. He was 
good to her. She likes him. He lives west of the school. My 
sister goes to see him. 

Words included are from lists of previous years. 
Marked simply upon spelling. 





Grade II. Spelling Test 


bird 


four nest 


box 


egg tree 


doll 


have wish 


fish 





DICTATION FOR GRADE II 

Will the principals please read the enclosed exercise through 
once, distinctly, then a sentence at a time for the children to 
write? Each sentence is to be read but once for the dictation. 

The large paper need not be used. Please send the papers 
to the office at once without ranking them. 

Dictation 

My mother says I may come to your house. Then you shall 
see my two dolls. One is big and one is little. I went home 
to get them. When school is over we will play with them. 

dictation (spelling) 

The accompanjHing dictation exercise for Grade I contains 
twenty words from the spelling list. 

Each sentence may be read loudly and distinctly twice only, 
and no questions are to be answered. The teacher should read 
the sentences, but in order to prevent misunderstandings and 
ensure exact uniformity in the way the test is given throughout 
the city, the principal is asked to remain in the room during the 
period. 

Each teacher is asked to mark at the top of each paper the 
number of words incorrectly spelled, taking into consideration 



104 Variation in the Achievements of Pupils 

only the twenty words underlined in the model. Attach to 
the front of each set of papers a slip bearing the summary of 
the work, as follows : 



School 6 Grade 1 Miss 

Number of papers with 

1 2 3 4 5 6 7 8 9 10 (or more errors) 
25 2302001200 (number of papers) 

Dictation 

1. I have a ball. 

2. The little star is in the sky. 

3. Do you want a red apple ? 

4. Baby has three dolls. 

5. I saw seven sheep. 

6. My father has a horse and a pig. 

7. My brother is in the house. 

8. There is a white egg in the nest. 

Please send the sets of papers with attached slips to the 
office as soon as possible; by Friday at the latest. 

Superintendent 



REPRODUCTION 

Will the principals please give the enclosed reproduction 
story in the third and fourth grade room which did not have the 
story of " The Cat and the Monkey " a few weeks ago? 

Please send the papers to the office as usual. 

For the third grade the title and the words creep, hungry, 
plenty, should be written on the board; for the fourth grade, 
the title only. 

The Grasshopper and the Ant 

Once there was a grasshopper who would not do any work. 
He liked to play in the sun. The little ant worked hard all 
day. At last cold days came. Then the ant had plenty of food 
in its warm house. The grasshopper had to creep under a 
stone. He was cold and hungry. 



APPENDIX III 

PRELIMINARY LIST OF COMPOSITION SUBJECTS 

How I like best to spend a day at home. 

How I spent the happiest day of last vacation. 

Write an account of how you will spend next Thanksgiving. 

Write an account of how you will spend next Christmas. 

My favorite amusement. 

What I should like to be and do when I am a man (or woman). 

The most exciting game I ever played. 

My favorite out-of-door play. 

Write a letter to your best friend telling him about the things 

most interesting to you. 
The most pleasant birthday I ever spent. 
The unhappiest birthday I ever spent. 
Write a letter describing a day at this school. 
A picture story. See type in Baker and Thorndike's Language 

Book, Part I, pp. 124-125. 
An incident in my summer vacation. 
How I made my garden. 
How I would spend one hundred dollars. 
How I would spend one thousand dollars. 
How I would spend one thousand dollars to please five persons 

who like different things. 
How I would spend one hundred dollars to please five persons 

who like different things. 



105 



106 Variation in the Achievements of Pupils 



NOTES ON THE TESTS 

The test in English composition might well be improved by- 
permitting each teacher to suggest the amount of money which 
in her judgment members of the class can best write about. 
This would have a tendency to make the results less compar- 
able than they are now but on the other hand might very well 
provide for greater freedom in composition. 

Every effort has been made to see that the tests in English 
composition as well as those in all other subjects were not drilled 
upon. Every precaution was taken by giving all the tests of 
one kind on the same day. For this reason it was absolutely 
impossible for the teachers in any grade to prepare their pupils 
in advance. 

The standards in handwriting discussed on pp. 35-36 pertain 
to ** muscular movement " writing. 



APPENDIX IV 
NOTES ON MEASUREMENT OF CLASS SIZE 

A 

TABLE I 

Records of 500 Children Selected from Systems A, B, C 
AND System E* 

Per cent of pupils in each group that reaches or exceeds the standard medians. 





Composi- 
tion 


Arith- 
metic 


Writing 


Vocab- 
ulary 


Grade V 

Small classes E 


70.0 
36.9 

72.15 
48.9 


42.4 
25.5 

87.34 
43.8 


61.0 
42.07 

59.5 
48.8 


68.6 


Large classes A-C 


21.8 


Grade VII 

Small classes E 


29.1 


Large classes A-C 


15.0 







TABLE II 

Records of 610 Children Selected at Random 

Per cent of pupils in each group that reaches or exceeds the standard 

medians 





Composi- 
tion 


Arith- 
metic 


Writing 


Vocab- 
ulary 


Graded 

Small classes 


39.23 
34.34 

40.1 
45.1 


37.3 
25.5 

55.5 
32.1 


45.0 
70.4 

40.0 
56.9 


70.9 


Large classes 


33.8 


Grade VII 

Small classes 


39.7 


Large classes 


29.3 







*These groups were selected deliberately that comparison might be made 
between a group of children in each grade that had been taught for four 
years in small classes with a group that had been taught for the same number 
of years in large classes. The school population is for all practical purposes 
identical. The teachers of the groups compared are roughly of the same 
ability. The comparison is not as fair as that presented in Table II. 

107 



108 Variation in the Achievements of Pupils 

The above tables are self-explanatory. One-half of the 
children have been taught in classes of 25-35 for four years* 
the other half have been taught in classes of over 40 for four 
years. When the records of individual pupils, to the number 
indicated in the tables, are compared with the tentative stand- 
ards suggested in Chapter III the superiority of the attainment 
of pupils who have been taught in small classes for a number 
of years is evident to a limited extent. However, as pointed 
out before, the presence of other factors is likely to exert an 
influence which cannot be explained by class size alone. 

Of course the systems are to some extent not comparable 
although the factor, character of population, does not appar- 
ently exert any influence when the results are tabulated in 
this way. Measured by the per cent of classes that reaches or 
exceeds the standards of Chapter III, the small class systems 
seem to be the most successful in grade five. But the fallacy 
of selection affects any interpretations such as those offered 
above because the small class systems here reported have more 
money to spend and this is generally true over the country. 
Thus such systems select the better teachers and provide better 
school facilities. 



B 

For the purpose of studying more completely the relation- 
ship of the size of class for the present year and for four years 
to attainment as set forth in Table VI, pp. 41-46, the classes 
were arranged in order of excellence in attainment and the 
attainments compared with the class sizes. 

When this is done and the attainment compared with the 
size of class for four years we find in grade five that small classes 
are superior in writing, range of vocabulary and spelling. Meas- 
ured by size of class for the present year the effect of class size 
is negligible except in the case of range of vocabulary. In grade 
seven, measured by size of class, for four years the small classes 
are decidedly superior in spelling, arithmetic and range of vocab- 
ulary. Measured by the size of class for the present year small 
classes have a decided effect only in arithmetic and spelling. 
In this grade the size of class seems to be a factor of less influ- 
ence than in grade five. 



APPENDIX V 

BIBLIOGRAPHY 

Scientific Management in Education 

The Measurement of Educational Efficiency 

Annual Report of School Committee. Newton, Mass. 1912. Vol. 73. 

Ayres, L. p. a Scale for the Quality of Handwriting of School Children. 
Bulletin of the Division of Education of the Russell Sage Foundation, 
1912, No. 113. 

Bachman, F. p. Attaining Efficiency in City School Systems. 

Annals of American Academy of Political and Social Science, May, 1912, 
pp. 158-175. 

BoBBiTT, John Franklin. Some General Principles of Management Ap- 
plied to the Problems of City-school Systems. Year Book of the Na- 
tional Society for the Scientific Study of Education. Part 1. Chicago: 
University of Chicago Press. 1912. 

Buckingham, B. R. Spelling Ability, Its Measurement and Distribution. 
Teachers College Contributions to Education, No. 59, 1913. 

— . The Courtis Tests. Journal of Educational Psychology, April, 

1914. 

Bulletin No. 1, Division of Reference and Research, Board of Education, 
City of New York. 

Cadbury, Edward. Experiments in Industrial Organization. New York: 
Longmans, Green, 1912. 

Cooke, Morris L. Academic and Industrial Efficiency. Bulletin No. 5 
of the Carnegie Foundation for the Advancement of Teaching. 

Cook, Henry R. The Standardization of School Statistics. N. E. A. 
Report, 1910. 

Commission on Economy and Efficiency. Message of the President Trans- 
mitting the Reports. Jan. 8, 1913. House Document No. 1252. Wash- 
ington: Gov't Printing Office. 

Cornman, Oliver P. Spelling in the Elementary School : An Experimental 
and Statistical Investigation. Boston: Ginn & Co., 1902. 

Cubberley, Spaulding and Others. The Portland Oregon, Survey. 
Board of Education, Portland, Oregon. 

Denver Report, 1908-1910. 

Education, December, 1913. 

Final Report of Committee on School Inquiry. 3 Vols. New York: Board 
of Estimate of New York City, 1913. 

FiNKELSTEiN, IsiDOR Edward. The Marking System in Theory and Prac- 
tice. Baltimore: Warwick & York, 1913. 

109 



110 Variation in the Achievements of Pupils 

Gray, Clarence Truman. Variation in the Grades of High School Pupils. 

Baltimore: Warwick & York, 1913. 
Hillegas, M. B. a Scale for the Measurement of Quality in English Com- 
position by Young People. New York; Teachers College, 1912. 
Hutchinson, J. Howard. School Costs and School Accounting. Teachers 

College Contributions to Education, No. 62, 1914. 
Journal of Political Economy, Jtily, 1913, Vol. XXI, No. 7. 
King, Wilford I. The Elements of Statistical Method. New York: 

Macmillan, 1912. 
Letter of U. S. Bureau of Education, March 27, 1914. 
Library Bureau, Catalog No. 3310. 
Munsterberg, Hugo. Psychology and Industrial Efficiency. New York: 

Houghton, Miff in & Co., 1913. 
Proceedings of S. P. E. E. for 1908. 
Psychological CHnic, Vol. VI, No. 1. 
Report of the Committee on Standards and Tests, Bulletin of the U. S. 

Bureau of Education, 1913, No. 13. 
Report of Committee on Uniform Records and Reports. N. E. A. Report, 

1911. 
Report of Public Schools of New Britain, Conn., 1910. 
Report of the Department of Superintendence. N. E. A. for 1912, St. 

Louis, p. 164. 
Rice, J. M. Scientific Management in Education. New York: Hinds, 

Noble and Eldredge, 1913. 

The FutiUty of the SpeUing Grind. The Forum, Vol. XXIII, pp. 

163-172 and 409-419. 

Educational Research: A Test in Arithmetic. The Forum, Vol. 

XXXIV, pp. 281-297. 

Causes of Success and Failure in Arithmetic. The Forum, Vol. 

XXXIV, pp. 437-452. 

Educational Research: The Results of a Test in Language. The 

Forum, Vol. XXXV, pp. 269-293. 

Language (continued): The Need of a New Basis in Education. 

The Forum, Vol. XXV, pp. 440-457. 
Scientific Management and Efficiency in College Administration. Pro- 
ceedings of S. P. E. E., 1913. 
School Review Monograph, No. 3, February, 1913. 
Simpson, B. R. The Correlation of Mental Abilities. Teachers College 

Contributions to Education, No. 53. 
Spaulding, F. L., and Others. Proceedings of the N E.. A., 1913, pp. 

247-279. 
Special Libraries. Efficiency Number. Indianapolis: The Special Libra- 
ries Association, Vol. IV, No. 5, May, 1913. 
Starch, Daniel. Handwriting, The Measurement of. Jour7ial of Ed. 

Psych., October, 1913. 
Strayer, G. D. and Thorndike, E. L. Educational Administration. 

New York: The Macmillan Co., 1913. 



Appendix V HI 

Strayer, Elliott and Judd. Expert Survey of the School System of 
Boise, Idaho. 

Strayer, G. D. Schedules and Record Forms in Report of Committee on 
Uniform Records and Reports. Bulletin of the U. S. Bureau of Educa- 
tion, 1912, No. 3. 

. City School Expenditures. Teachers College Contributions to 

Education, No. 5. 

Taylor, F. W. Scientific Management. New York: Wiley & Sons, 1912. 

Thompson, Mary E. Psychology and Pedagogy of Writing. Baltimore: 
Warwick & York, 1911. 

Thorndike, E. L. The Measurement of Achievement in Drawing. Teach- 
ers College Record, November, 1913. 

Mental and Social Measurements (second edition). New York: 
Teachers College, 1912. 

Educational Diagnosis: Vice-Presidential Address. American Asso- 
ciation for the Advancement of Science, 1912. Science, N. S., Vol. 
37, Nos. 943 and 946. 

Heredity, Correlation and Sex Differences in School Abilities. 
Columbia University Contributions to Philosophy, Psychology and 
Education, Vol. XI, No. 2. 

Handwriting. Teachers College Record, March, 1910. 

Wallin, J. E. Wallace. Spelling Efficiency in Relation to Age, Grade 
and Sex, and the Question of Transfer. Baltimore: Warwick & York, 
1911. 

Whipple, Guy Montrose. Manual of Mental and Physical Tests (second 
edition). Vol. I. Baltimore: Warwick & York, 1914. Also first edition, 
1910. 



Miscellaneous Books and Articles on Standardization of 
Education 

Babcock, K. C. Accredited Secondary Schools in the United States. Bul- 
letin of the U. S. Bureau of Education, 1913, No. 29. 

Broome, E. C. A History of College Entrance Requirements. Columbia 
Contributions to Education, 1896-1897. 

Courtis, Stuart A. Standard Tests in English. Elementary Schoo 
Teacher, 14: 374-92, April, 1914. 

Henderson, J. L. Admission to College by Certificate. Teachers College 
Contributions to Education, 1912, No. 50. 

High School Manual. University of Illinois. 

Hooper, Cyrus L. The Cornman and Wallin Tests. Educational Bi- 
monthly 8:28-41, October, 1913. 

Judd, Charles H. Reading Tests. Elementary School Teacher, 14:365- 
73, April, 1914. 

KiNGSLEY, Clarence D. College Entrance Requirements. Bulletin of the 
U. S. Bureau of Education, 1913, No. 7. 

Montgomery, L. J. A Writing Test. Educator-journal, 14:479-83, May, 
1914. 



112 Variation in the Achievements of Pupils 

Reports of the Illinois High School Conference, 1905-1913. 

School Surveys. Plans for Organizing School Surveys with a Summary 

of Typical School Surveys. The Thirteenth Yearbook of the National 

Society for the Study of Education, 1914. 

Practically all of the surveys listed in the report have been consulted. 

The list is not repeated here as the reader interested in school surveys 

will consult this excellent report. 
Smith, Arthur O. Preliminary Report of the Lough- Smith Tests in Arith- 
metic. American Education^ 17:410-11, March, 1914. 
Strayer, G. D., and Others. Survey of Butte PubHc Schools. Butte ^ 

Montana, 1914. 
The Reorganization of Secondary Education. Committee of the N. E. A. 

Bulletin of the U. S. Bureau of Education. 1913. No. 41. 



General Bibliography 

Annual Report of the Superintendent of Schools, Newark, N. J., 1912. 

Ayres. Laggards in Our Schools. New York: Charities Publication Com- 
mittee, 1909. 

. Seven Great Foundations. New York: Russell Sage Foun- 
dation. 1910. 

Bray, S. E. School Organization. Second Edition, Revised and Enlarged. 
London: W. B. Clive, 1911. 

Building Code of the State Board of Education of New Jersey, 1913. 

Bulletin of the United States Bureau of Education, 1910, No. 5. 

Bulletin of the United States Bureau of Education, 1911, No. 14. 

Bulletin of the United States Bureau of Education, 1911, No. 4. 

Dresslar, F. B. School Hygiene. New York: The Macmillan Co., 1913. 

'■ — . The American School House. Bulletin of the U. S. Bureau 

of Education, 1910, No. 5. 

Button and Snedden. Administration of Public Education in the U. S. 
Revised Edition. New York: The Macmillan Co., 1912. 

Fifteenth Annual Report of the City Superintendent of Schools of New 
York City, pp. 41-44, July 13, 1913. 

Final Report of the Committee on School Inquiry, 1911-1913. 3 Vols. 
New York: Board of Estimate and Apportionment, 1913. 

Hall, G. Stanley. Aspects of Child Life and Education. New York: 
Ginn & Co., 1905. 

^^ , Adolescence. Vol. II. New York: D. Appleton & Co., 1907. 

t\ Holmes, W. H. School Organization and the Individual Child. Grading 
and Special Schools. Chap. XIII. Worcester, Mass.: The Davis 
Press, 1912. 

Ladd, G. T. and Woodworth, R. S. Physiological Psychology. New 
York: Charles M Scribner's Sons, 1911. 

Landon, Joseph. School Management. London: Kegan, Paul, French & 
Co., 1883. 

Laws of New Jersey, 1911, Article X. 



Appendix V 113 

LowRY. Seventh Yearbook of N. S, S. E. 

MacCurdy, J. L., Dr. American Physical Education Review, Dec, 1913. 

MacDougall, William. Introduction to Social Psychology. Boston: 

John W. Luce & Co., 1911. 
Manual of the Board of Education, City of New York, 1911 and 1914. 
Meyers, Garry C. A Study in Incidental Memory. Columbia University 

Contributions to Philosophy and Psychology. Vol. XXI, No. 4. 
Monroe, Paul. Cyclopedia of Education. New York: The Macmillan Co., 

1913. 
. Text Book in The History of Education. New York: The 

Macmillan Co., 1906. 
Payne. Public Elementary School Curricula. New York: Silver, Burdett 

& Co., 1905. 
Pedagogical Seminary, June, 1905, pp. 214-230. 
Pedagogical Seminary, Vol. 7, No. 1, p. 13ff. 
Perry. The Management of a City School. New York: The Macmillan 

Co., 1910. 
Psychological Clinic, Vol. VI, No. 1, March 15, 1912, pp. 1-12. 
Psychological Clinic, Vol. Ill, No. 7, pp. 206-212. 
Psychological Clinic, May 15, 1914, Vol. Ill, No. 3, pp. 82-90. 
Red Codes of N. U. T. for 1908-1912. 

Report of the School Committee, Boston, Mass., 1910, p. 72, Sec. 292, 
Reports of the Carnegie Foundation for the Advancement of Teaching, 

1908, 1909, 1910, 1913, 1914. 
Rules and Regulations of the Board of Education, San Francisco. Adopted 

December 28, 1910. 
Rules of the Board of Education of the School District of the City of Cin- 
cinnati. Adopted April 17, 1905, p. 83. 
Rules and Regulations and Course of Study, Minneapolis Public Schools, 

1910-1911, p. 12, Sec. II. 
Science, New Series, Vol. 31, No. 803, pp. 761-767. 
Snedden and Allen. School Reports and School Efficiency. New York: 

The Macmillan Co., 1908. 
Standards of the Report of the Commission on Accredited Schools. North 

Central Association of Colleges and Secondary Schools, 1912. 
Teachers College Alumni Bulletin, 1913. 
The Cost of English Teaching. Bulletin of Sub-committee of N. E. A. 

Committee on the Reorganization of Secondary Education. 
Thomas, W. I. Source Book of Social Origins. Chicago: University of 

Chicago Press. 
Thorndike, E. L. Animal Intelligence and Other Essays. New York: 

The Macmillan Co., 1911. 
. Educational Psychology. Revised Edition. 3 Vols. New 

York: Teachers College, 1913. 
Twenty-third Annual Report of Salt Lake City. 
United States, Reports of the Commissioner of Education, 1903-1913, 



114 Variation in the Achievements of Pupils 

Van Denburg, Joseph K. Causes of the Elimination of Students in Public 
Secondary Schools of New York City. Teachers College Contribution^ 
to Education, No. 47. 

Wilson, J. M. Standardization of Janitor Service. Report of the N. E. A. 
Dep't of Superintendence, 1912, p. 138. 

A Good Bibliography on Measurement is Found in the Fol- 
lowing Titles which are Quoted in this Bibliography: 

(a) The Thirteenth Yearbook of the National Society for the Study of 

Education. 

(b) Bulletin No. 1 of the Bureau of Reference and Research, Board of Edu- 

cation, New York City. 

(c) Studies Reported in Educational Administration, by Strayer and Thorn- 

dike. 

(d) Mental and Social Measurements (second edition), by E. L. Thorndike. 

(e) Tests for Measuring the Efficiency of School Systems. Bulletin of the 

U. S. Bureau of Education, 1913, No. 13. 

These references contain also bibliographies on the measurement of 
intelligence. For this reason, an extended bibliography on these phases 
of measurement is not included in this list. 



A bibliography of text-books which discuss briefly the question of class 
size in the United States and references to the reports of foreign countries 
are not included in this list. 



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